Required documents for an EEA Family permit for tourism

Question

My EEA wife and I (non-EU) live in my country (outside the EU) and we are planning to travel to the UK for few weeks as tourists. We are planning to provide:

1. My current and old passport.
2. Marriage certificate (original + English certified translation).
3. My wife's certified copy of current and old passport (she changed her name to mine, but in our marriage certificate only her maiden name is mentioned).
4. Proofs of our relationship and our life together.
   -WhatsApp, Skype, Facebook, Viber, etc.
   -Photos from our trips, life events, etc.
   -Paper from my bank as she has access to my account and we share it.
   -Scans of our health insurance because she's added to mine, provided by my employer.
   
5. Booking from hotel where we stayed for our honeymoon, and other tickets.
6. A letter from work, which says that my holiday was approved for the duration of our planned trip.
   
7. Booking from booking.com, which shows the place where we are going to stay during our trip.
   

As I said, we are planning to go there for a trip (2 weeks). I have some savings on my bank account, from which I am planning to pay for tickets etc. Also, my wife have savings but in cash (she brought money from her home country. Her family gave us cash ($) when they came to visit us a few months ago. We are not planning to put these on our bank account because it will be hard to withdraw any other currency than my national).

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?
2. 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? I don't want them to treat my application as I am saying that I depend on my wife (because in this case we should show evidence).
3. Can applying like that, for a trip, providing only the documents I mentioned, be successful? (I am afraid of rejection on reasons they doubt we have enough money to afford these 2 weeks, even when I know that by EU law they can't ask for it).

Edit per Karim's clarification (in answer, deleted):
My wife is not British. She's Polish. Also we don't have kids yet, and we got married December 2017. In relation since beginning of 2016.

Answer 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.