Are you absolutely confident in the security of bitcoin client that you use?
Are you 100% confident in the security of your banking system? Theoretically, the principles are the same. Bitcoin is in active development, and is open source meaning that if a vulnerability is detected, then it should hopefully be patched quickly. Bitcoin has in the past had several vulnerabilities of various degrees, all of which it has recovered from. There was basically a vulnerability in the early days which allowed creating new coins,
Are you absolutely sure in the security of OS that you use for the bitcoin client?
To a degree, yes. There's various vulnerabilities found in all operating systems somewhat regularly, just like any other piece of software. Your phone has been vulnerable , and so has the software you are using on this very forum. The point is, and this is an extension to your first question; there is no avoiding vulnerabilities in software, and therefore not only is Bitcoin under threat from that, but also the operating system you use to login to all your accounts, including your banking account if you use online banking. Also, even if you don't use online banking personally, your bank likely uses the same operating systems that we can get our hands on, probably some distribution of Linux. Even if its a custom coded operating system, it can likely be attacked the very same way as any operating system available to consumers.
its also worth mentioning that, you can actually make a Bitcoin wallet via various different methods, some of which don't require being online which significantly reduces the chances of malicious attacks, unless the attacker has physical access to your device.
Are you always confident that the binaries you download do not contain a backdoor?
Depends on binaries you are specifically talking about. However, generally if the code is open source then you can verify it, or get someone else to verify it for you.
Are you absolutely confident that when you download a repository from a github, you download the original code? Do you check the hash every time?
Yes, this is including, but not limited to the operating system I use.
Are you absolutely confident that open source guarantees no backdoors inside? You probably read it all after downloading from github?
No, it guarantees nothing, Although, the chances of a malicious program being open source, is significantly less so than it being closed source. Basically, the code can be verified, but lets be honest not all of us understand that specific language or we don't have the time since programs can literally be hundreds of thousands lines of code, and therefore to an extent you are relying on a collective effort to verify that the code is clean, and safe. Generally, you can vet the code in specific areas, for example what happens when you enter the private key, is it logged anywhere or sent to someone's email address etc.
Not to mention, there are dedicated organizations out there in verifying open source content. Yeah, you are again relying on another third party, but without actually having the time, and knowledge yourself you are pretty much limited to giving some sort of trust to the collective. However, banks don't have this option, and you must entirely put your trust in them to manage your money, invest your money, and to keep patching any vulnerabilities that they find.
There is one exception to this, and that is generally the more developed countries tend to have a protection limit, that if the bank goes bust for example, they will reimburse a set amount. I think in the UK its 85k. You of course, don't have this in Bitcoin, but other than that in every other sense, traditional currencies are just as susceptible to attacks than Bitcoin. You could even argue more so, since there's physical location that can be attacked not just a digital one.
One hole anywhere is enough to lose all your money. You cannot check everything. Organizations that will use cryptocurrencies will not be able to verify everything. Bitcoins are very easy to steal due to the human factor.
If bitcoin becomes widespread there will be a great interest in finding and creating such vulnerabilities
This is literally true for everything. The majority of the people in the world are already using a system which relies on computers, and are therefore have the same concerns. The majority of people now use online banking, not only that they are using it on phones, that they install apps on which have access to varying amounts of information, and they browse on that same phone, they do everything on that phone. When you own Bitcoin, you are basically removing the third party element, so you are more inclined to protect your assets. Therefore, you generally aren't going to be storing your main wallet, on a live machine. At least, it isn't recommended.