Should we question all knowledge from all sources?
Yes. That's the only way one can rationally have confidence in one's beliefs.
Regarding doubting reason, reason can't be proven, it is perceived and judged instantly by our logic, but what if our logic is not true?
Not sure I quite got your question.
But different people will reach different conclusions given similar or the same information. So it stands to reason that the reasoning ability of one of those people is flawed (and you necessarily are one of those people for a wide range of beliefs).
If you don't question your own reasoning ability, it's much less likely, or impossible, that you'd find flaws in your own reasoning and you can't rationally be confident that your own reasoning ability is flawless.
We've come up with some principles of reasoning and we see how well these work or don't work when applied to different ideas. This can serve as evidence for or against you having good reasoning ability.
And yes, it can be quite hard to accurately judge whether your reasoning ability is flawed or not, given that you're judging this with your reasoning ability, and many people have quite a strong aversion to being wrong and have strong emotional attachments to some of their beliefs (meaning they'd be less open to seeing a flaw in their reasoning if their belief relies on that flaw).
Did anyone ever question that much?
It's not that much.
You should proportion your questioning to:
- The importance of the belief.
- Whether there are other plausible competing ideas. This can be judged to some degree by seeing whether a decent amount of people hold competing beliefs, but it might also be that the truth hasn't been discovered or popularised yet. And I don't mean you should go with what the majority thinks, but rather just that if a decent proportion of the population believes something, that might merit investigating it.
- How well the evidence supports the belief compared to competing beliefs. But this is something you'd likely only know (and not deceive yourself about) after you've done some sincere questioning.
As an example, the existence of an afterlife and whether we dedicate our lives to some deity would be quite important, and there are certainly competing ideas and people on various sides claiming they have reasonable justification for belief. So regardless of which side you're on, you should probably question that to some degree.
The composition of a star on the other side of the universe, on the other hand, is probably not that important to anyone except astronomers, and there aren't many plausible competing ideas, so you can probably just go with what the scientific community says until you have a reason to question that belief.
What definitely proves or disproves one's doubts?
Nothing definitely proves or disproves anything.
But given sufficient evidence, we can be 99%+ confident that some belief is true.
There's always some uncertainty, but this mostly just means you should be open to the possibility that you're wrong.
If we can doubt beliefs, why do we all depend on them and behave according to them?
Because we've evaluated the evidence and concluded that what we believe is the most likely of all the competing ideas.
If you're not much more certain of your belief above others, then you should probably investigate further (to become more certain, of what you believe, or a competing idea) or account for plausible alternatives in your actions. If you're fairly sure that you turned off the oven, but there's a good chance that you didn't, it's probably best to check, because if you did turn it off, you (generally) only lose a bit of time, but if you didn't turn it off, checking is much more beneficial.
* I prefer "question" above "doubt", because questioning is an action, whereas doubting is how you feel about things you're uncertain about (at least by my definitions). You don't typically feel uncertain about a belief until you start questioning it, and you don't need to feel all that uncertain about a belief (but still be open to the possibility that you're wrong) after you've questioned it to a point where the belief has been sufficiently validated.