Popper is an excellent starting point for understanding what is or isn't science. His falsifiability criteria is basically a precondition, but even more important is that the practitioners of science need to have an attitude embracing falsifiability -- IE look for and accept falsifications of one's views.
For example, two relevant cases are Creationism and Intelligent Design. Both are testable claims about our world. Creationism is pretty easily refuted by the observed evolution of life, plus the timelines observable in geology and astronomy. Intelligent design makes testable predictions about design stability and commonality, and optimality, which also are refuted when one examines details of structures and evolution, and the part of randomness in life. What makes these NOT scientific hypotheses, is that their advocates do not embrace the scientific methodology in evaluating them.
You ask about quantifying degrees of predictive power -- Popper attempted to do this, over decades, but his effort to quantify either predictability or confidence through numerical processes failed. The alternative is a judgement call, as to whether a community is applying the scientific attitude to their research programme. The best explication of this process is from Imre Lakatos, summarized here: http://people.loyno.edu/~folse/Lakatos.html Lakatos too tried to quantify his criteria of progressive/regressive, but that quantification also was flawed. As with much in the world, we must rely upon a consensus of reasonable observers to judge the boundary of science/non-science.
You also asked questions about two areas of current scientific inquiry -- abiogenesis, and a multiverse. These two subjects reveal yet more about what is or isn't science.
Abiogenesis is clearly a scientific hypothesis, and it has been a scientific field of study for ~80 years. The hypothesis makes a number of predictions -- including that our world's history should have been fertile for chance processes to produce life, and that the chemical path to life is possible. The first of these predictions was dramatically confirmed in the Urey-Miller experiment. The second -- has a much rockier history. Most of the Abiogenesis research since Urey Miller has been discoveries of just how difficult that chemical pathway IS. Chirality, and poisoning with closely related compounds, basically prevent any build-up of proteins or RNA in natural processes. And for RNA in particular, the UV light that is needed to create one building block also destroys the growing strand. Plus lipid membranes are lethal to a developing metabolism inside, unless they are semi-permeable -- and basic lipid membranes are not semi-permeable. The best book I have seen on this is Dyson's Origins of Life. Dyson considers the RNA path too complex, and lipids too problematic to start, so hypothesizes that proteins metabolism in free environments evolved first, then was lipid-captured, then taken over by a basically parasitic RNA. This strikes me as an almost equally implausible sequence to RNA first.
Note the response of Abiogenesis community is to narrow over and over the environments that Abiogenesis can happen in. The RNA precursors need UV, but RNA cannot have any, but SOME energy source is needed to fuel the strand build-up, hence a deep undersea vent is proposed (the precursor can be formed on the surface, then fall to the vent). But to overcome chirality, a clay banks which bonds the proteins and RNA in only one direction is proposed. This is now a TINY FRACTION of the massive pool of oceans that Urey-Miller suggested were available --- the number of monkeys at typewriters is reduced by something like 10^10 or worse. This raises a throughput question for abiogenesis -- is there sufficient mass of reaction events, and time for life to have abiogenesised in the time it appears to have? Note that fully formed stromatiolite mats are found in rocks from 4.4 billion years ago -- IE multicellular colonies appeared within 300 million years of the oceans cooling.
When one looks at the logic of life complexity -- a single bacteria cells is about half as complex as an elephant. Evolution SINCE 4.4 billion years ago took 4.4 billion years to get to elephant-level of complexity from half that level. That the first half of the complexity development took place is 1/15th the time of the 2nd half -- despite the 2nd half basically having the entire biomass to work with, while the first half only had 1/10^10 of that biomass (the clay surfaces around the vents) -- basically abiogenesis research since Urey-Miller has accumulated a case that Abiogenesis is increasingly improbable.
When I have discussed this with materialists, they typically say that there is no other alternative, hence they have faith that abiogenesis will get there eventually. There are two other alternatives -- panspermia, and non-material causes. Panspermia has the same logic issues, but by putting it in TBD environments, it may not have the timeline constraints or volume constraints that Earthly abiogenesis has. Non-material causes can include an "organizing principle for the universe" which some materialists such as Christian De Duve and Stuart Kauffman hypothesize. Or it could be a spiritual intervention. The REJECTON out of hand of these sorts of alternatives, when Abiogenesis seems to be a regressive research programme, arguably is making the abiogenesis community increasingly iffy on being "scientific". It is held to as an article of faith among materialists.
Multiverse is a similar area of concern for materialism and science. The multiverse used to be rejected out of hand, as untestable speculative piffle. THEN -- the realization took hold in the cosmology community that our universe is remarkably unlikely -- that it appears to be Fine Tuned for life. The probability calculations that one derives form the Standard Model suggest that there are multiple free variables (about 30) in our physics that can only support life within fractions of their range between 1/10^2 to 1/10^30. This is supporting evidence for our universe being a product of deliberate creation (note Creationism IS potentially a science hypothesis, depending on how one handles it). It is not GOOD evidence for intelligent/theistic creation, as our universe is poorly optimized for life, but still, it is somewhat related to what ID would predict. Non-theist Cosmologists cast about for some way to explain "apparent fine tuning", and realized that a very large Mutiverse would do the trick. An excellent discussion of this process is in Susskind's The Cosmic Landscape. I have a review here: https://www.amazon.com/gp/customer-reviews/R3JVQDAK1408BR/ref=cm_cr_getr_d_rvw_ttl?ie=UTF8&ASIN=0316013331
Most of Susskind's Cosmic Landscape is untestable in principle, which makes it highly relevant to your question. But it is not entirely untestable, as it has failed two tests, as noted in my review, which required kluges to fix. It also has NOT proven to be productive/useful for experimentalists, which is the basis for Smolin's critique. Sting/theory/multiverse/cosmic landscape therefore appears to be a regressive research programme, which once more materialists are holding on to, as there is no other better alternative which is compatible with materialism.
What you have hit upon, and seems to be a motivation for many of your questions on science, is that there IS a faith-view involved behind many scientists thinking.
That view is materialism. Materialism is generally not treated as a science hypothesis. If it were, then the Hard Problem of Consciousness, and the nature of both information and abstract objects, would constitute refuting test cases, while much of quantum mechanics would bring the coherence of the hypothesis into question. That faith-based assumption of materialism skews the reasoned response of many scientists to a variety of science fields, including both cosmology and abiogenesis.
