Upvote:1
By my understanding according to EU law we don't have to provide any bank statement (mine or wife's) or proof of having money (even when we put info in my application that we do have savings) as none of us is living in the UK. Is it true?
You only have to provide this if you live in the UK and are neither working nor studying. So in your case, you are correct: you do not need to provide it.
Can I write in my application that my wife will sponsor this trip, even if in daily life we share the budget and no one is a sponsor?
Sponsorship in this case concerns nationality, not finances. The answer is therefore yes, your wife is the sponsor.
Can applying like that, for a trip, providing only the documents I mentioned, be successful?
Yes, but you might want to avoid submitting superfluous documents. Items 5 and 6 in your list are unnecessary, and item 4 is only necessary if there is reason to suspect that you are in a marriage of convenience. This suspicion should generally arise only if your marriage is less than two years old and you have no children.
There is one other thing to mention: if your wife is a British citizen, then she is not an "EEA national" under UK law, in which case you should apply for a standard visitor visa instead.