Is the existence of qualia generally considered an unresolved problem by philosophers? Is there a consensus on its nature or whether it can be studied at all?
Purely philosophically, consciousness is stuck between two schools of thought (generally, since each idea also have different sub-theories).
See more on the wikipedia article on consciousness, especially the mind-body problem.
One is the materialist/realist idea, where consciousness is a product of cause and effect by random events dating back to the beginning of the universe with the big bang.
The other is the theist/deist/idealist idea, where consciousness is something beyond the physical, and has the power to influence our brain. Each school of thought presupposes something beyond the idea itself. Materialism presupposes that there is just matter and energy across time, and nothing beyond that. The converse presupposes that there exists some metaphysical higher plane outside of the purely physical, and that our mind/consciousness is either completely or partly residing within this higher plane, interacting with the physical plane.
The train of experiments that had it's outspringing in the original double-slit experiment seems to suggest that the mind is not only responsible for influencing the brain, but that it is quite literally responsible for manifesting it and the world around us. The mind might actually be more real than matter. In a way. InspiringPhilosophy on youtube has a video about this, where he goes through and explains the studies, with clips from interviews with experts.
I am not sure if the issue is resolved or not though. I think we are getting close.
Consciousness is not a problem in philosophy. It is only a problem in university philosophy, where it is not studied. The study of consciousness is called Mysticism or Yoga. Academics just talk about it and argue about their speculative theories.
Nobody in the perennial tradition talks about the 'problem of consciousness'. Rather, they talk about the problem of ignorance.
An answer to your question would require giving a bit more detail since the problem has many aspects and may be formulated in various ways. Chalmers' 'hard' problem, for instance, is easy to solve, but other related problems are more tricky.
“Issues of concern in the philosophy of consciousness include whether the concept is fundamentally coherent; whether consciousness can ever be explained mechanistically; whether non-human consciousness exists and if so how it can be recognized; how consciousness relates to language; whether consciousness can be understood in a way that does not require a dualistic distinction between mental and physical states or properties; and whether it may ever be possible for computing machines like computers or robots to be conscious, a topic studied in the field of artificial intelligence.” (Wikipedia Contributers)
"Philosophical opinions about the Hard Problem are so diverse and strongly felt by their supporters, that even attempting a possible scientific approach to solving the Hard Problem may sometimes feel like stepping on a philosophical “third rail”. This is because philosophers vary passionately in their views between the claim that no Hard Problem remains once it is explained how the brain generates experience, as in the writings of Daniel Dennett, to the claim that it cannot in principle be solved by the scientific method, as in the writings of David Chalmers." (Grossberg, S)
Depending on what philosophy you ascribe to it may or may not be considered a resolvable problem. For dualism something supernatural would have to influence brain function. However, there isn’t any empirical evidence to support this case. Meaning if you ascribe to a dualistic philosophy than you may not consider it a resolvable problem. But, if you ascribe to empirical philosophy than you might consider it to be solvable if studied using the scientific method.
"Is the existence of qualia generally considered an unresolved problem by philosophers?"
"Philosopher and cognitive scientist Daniel Dennett once suggested that qualia was 'an unfamiliar term for something that could not be more familiar to each of us: the ways things seem to us'".
"Much of the debate over their importance hinges on the definition of the term, and various philosophers emphasize or deny the existence of certain features of qualia. Consequently, the nature and existence of various definitions of qualia remains controversial due to qualia not being a pragmatically verifiable matter." (Wikipedia Contributors)
Science has invested quite a bit of effort into understanding the brain and how it functions. There is evidence to suggest that our brains function as very dynamic, intricate, and coordinating systems of neurons that give rise to particular types of perceptions through computation.
"Neural signals combine, dissolve, reconfigure, and recombine over time, allowing perception, emotion, and cognition to happen." (Demerzi, A., et al.)
The trouble for neuroscience is figuring out how the information gets integrated to create one cohesive experience. There was a theory for this proposed by Kristof Koch and his team that the claustrum, located in the insular cortex, may be responsible for this integration. However, recent studies suggest that while it's necessary for conciousness it may just act to orchestrate and direct brain signals but not integrate them. (Frohlich, J.)
"There are several theoretical models of consciousness. The Integrated Information Theory (IIT) has been proposed by Giulio Tononi. It postulates that one can be conscious of multiple things and that they are highly integrated. For example, one can be conscious of uncountable scenes from all the movies one has seen. Experiences are highly integrated. Whereas family photos in a laptop are usually unlinked, they are very much integrated in the brain with memories. A number of neuronal circuits are involved in the integration of all the conscious experiences. This can be further estimated mathematically. Another model has been proposed by Jean-Pierre Changeux and Stanislas Dehaene. Whenever we become conscious about something it can be retained in the working memory. It can then be processed in the global neuronal workspace (GNW), a number of long neurons interconnecting various hubs in the brain. In this way the impression from any sense organ such as a familiar face or voice, a taste or a smell can be associated with old memories and integrated. This can be tested by a special technique called ‘masking’. A face is shown briefly followed by a mask. It is registered in the primary visual cortex but the subject does not seem to be aware of it. If it is shown for a little longer, hubs in the whole brain are activiated, particularly the GNW. This activation is associated with the presence of event-related potentials which have been demonstrated in 5-, 12- and 15-month-old infants. Thus conscious perception is already present in infancy." (Langercrantz H.)
References and further reading:
Demertzi, A., et al. (2019). “Human Consciousness Is Supported by Dynamic Complex Patterns of Brain Signal Coordination.” Science Advances, American Association for the Advancement of Science, advances.sciencemag.org/content/5/2/eaat7603.full. http://advances.sciencemag.org/content/5/2/eaat7603
Frohlich, J. (2017). "What the Heck is a Claustrum." Psychology Today. https://www.psychologytoday.com/us/blog/consciousness-self-organization-and-neuroscience/201702/what-the-heck-is-claustrum?amp
Grossberg, S. (2017). Towards solving the hard problem of consciousness: The varieties of brain resonances and the conscious experiences that they support. Neural Networks, 87, 38-95. doi:10.1016/j.neunet.2016.11.003. https://www.sciencedirect.com/science/article/pii/S0893608016301800
Havlík, M. (2017). Missing piece of the puzzle in the science of consciousness: Resting state and endogenous correlates of consciousness. Consciousness and Cognition, 49, 70-85. doi:10.1016/j.concog.2017.01.006. https://www.sciencedirect.com/science/article/pii/S1053810017300338?via%3Dihub
Lagercrantz, H. (2014). The emergence of consciousness: Science and ethics. Seminars in Fetal and Neonatal Medicine, 19(5), 300-305. doi:10.1016/j.siny.2014.08.003. https://www.sciencedirect.com/science/article/pii/S1744165X14000547
Paller, K. A., & Suzuki, S. (2014). The source of consciousness. Trends in Cognitive Sciences, 18(8), 387-389. doi:10.1016/j.tics.2014.05.012. https://www.cell.com/trends/cognitive-sciences/fulltext/S1364-6613(14)00133-8?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS1364661314001338%3Fshowall%3Dtrue
Pierson, L. M., & Trout, M. (2017). What is consciousness for? New Ideas in Psychology, 47, 62-71. doi:10.1016/j.newideapsych.2017.05.004. https://www.sciencedirect.com/science/article/pii/S0732118X15300039
Van Gulick, Robert, "Consciousness", The Stanford Encyclopedia of Philosophy (Spring 2018 Edition), Edward N. Zalta (ed.). https://plato.stanford.edu/archives/spr2018/entries/consciousness/
Wikipedia contributors. (2019, February 27). Consciousness. In Wikipedia, The Free Encyclopedia. https://en.wikipedia.org/w/index.php?title=Consciousness&oldid=885332111
Wikipedia contributors. (2019, March 5). Qualia. In Wikipedia, The Free Encyclopedia. https://en.wikipedia.org/w/index.php?title=Qualia&oldid=886256386
See https://qualiaresearchinstitute.org. It has very interesting things about this topic. But from just researching, it is trying to be resolved, but is still unresolved. Otherwise, I think science will help more with question than just pure philosophy.