An initial note: To claim that science is "better" than religion implies that science is trying to answer the same questions as religion. Many would argue that that is not the case. See Stephen Gould's Non-overlapping magisteria or Karen Armstrong's distinction between Logos and Mythos.
It is still possible to argue that science and religion are both trying to answer the same or similar questions. For example modern cosmology's big-bang vs the Biblical and Quranic accounts of creation.
Question 1. Why is science better than religion even though the currently accepted scientific theory may be proven to be wrong in the future? How can we trust that our current theories aren't wrong?
The answer to this is: We can't trust that our current theories are correct, and that is exactly what defines science. Ideally, the scientific attitude is to accept that a theory, no matter how widely accepted and how well supported by experimental evidence, can eventually be proven false and replaced by a another theory. This is the concept of Falsifiability proposed by Karl Popper.
A scientist, when stating that they believe that Einstein's theory of relativity is true, should also state the following "under what conditions are you willing to abandon relativity?" - this isn't to say that relativity is false, only that it can be proven false - i.e. there is a possible experiment whose result might show that Einstein's model is wrong and another one should be proposed instead.
Contrast this to the religious attitude: When somebody has faith in God, nothing, no set of real world facts or new experiments is going to convince them otherwise. When confronted with facts that might contradict their belief in a benevolent God (the holocaust, the death of children in Syria, hurricane Harvey,...) they would simply reply that "there must be a reason","God works in mysterious ways", etc...and continue believing none the less. One can say that the concept of God is not falsifiable (see this post).
Another way of looking at it is the following: Religion is backward looking, it assumes the truth is already established and known, we just need to go dig it up from the right sources. Science (again ideally, not always in practice) is forward looking, it assumes that the complete truth is not known yet, and that more shall be revealed.
It should be noted that there are some problems with the falsifiability approach to define science, but discussing them would make this post too long. Look up underdetermination, Quine, Kuhn and Feyearbend on the philosophy and demarcation of science.
Overall, Popper's approach provides a working way of distinguishing science and religion, insofar as they are trying to address the same questions. In this sense, science is better than religion, because it is flexible and is willing to admit its mistakes, while religion is dogmatic and doesn't allow for self-correction.
Question 2. Can we believe certain scientific theories/results even if we personally don't understand most of the concepts/theories ourselves? Why? Isn't this similar to how people put their "faith" in god? Aren't we placing our "faith" on the experts?
This is almost a duplicate of How can an uneducated but rational person differentiate between science and religion?
There is a pragmatic response to this:
You have an illness, the priest asks you to pray for your illness to be cured, while the doctor prescribes you medication to cure your disease. Who do you trust and why?
How many cell-phones, laptops and airplanes have shamans and gurus made based on their theories?
Answer those question and you will have an answer to your question.