kengolive

There is no tax on owning assets as you seem to imply? You are taxed on income on those assets, and capital gains of you sell them.
Reporting requriements for FBAR are cash and securities accounts, if over a certain minimum in aggregate (I can't remember what the threshold is) then you need to report all accounts even if an individual one is below the limit. But the requirements are all clearly spelt out on the IRS website.

No, you dont have to do this
Once u r approved for a visa, u will be informed to come back to the embassy to collect ur passport.
They r not sending passports by courier

That age is not a problem, and you qualify via education, so the only potential issue at interview could be public charge concern. What gets asked varies by embassy - so you may (or may not) get asked what you do now, what you plan to do there, whether you have any savings/assets, whether you have someone who will provide an affidavit of support, etc.

They wouldn't deny you a visa due to child custody reasons.

Where are you planning to be interviewed? Armenia? Here we just go to the regional notary center and get a stamped paper from the custody parent, that he/she hands the care of the child to the other parent who will be travelling blah, blah, blah, and it works for the embassy, but I don't know if you do that in Iran, so if it's excepted in your country, don't worry about the consulate, just get it and bring over.

You didn't put your country etc. You also didn't specify which parent you are (your avatar looks male, and your quoted legal document says the wife has custody, so I'm not sure: do you have the custody?)
Anyway, the EU has this policy that they won't allow one parent to remove the child from the country without the other parent's approval (I know because I've come face-to-face with it and almost missed a wonderful vacation because I was 17 and nobody notified us about this). I'm sure other places have similar rules.
Not sure how it works if only one parent has custody, but it's definitely a thing to ask both the US consulate and the border patrol or whatever authority allows people to exit/enter the country. Because, the US might not care but your country might, or the opposite might be true. The consulate will also tell you if you need that document to the interview.

Don't worry about any of it. You don't need to show his educational docs, only yours. Any info you need to update can be done at interview but you probably won't need to at all. The important thing to them is that he is a minor child accompanying you so birth certificate and passport really all they need for him.

You have two options for travelling later: 1 is "follow to join" where she gets a DV visa as well (although later than you do) so must still get by 30 Sept of your DV year and travel within 6 months of the visa (or less depending on visa expiry). The other option is that she does not get a DV visa and you sponsor her later. That will take a longer time and be more expensive. How long will depend on when you do it, ie if she is still under 21 or not. If she gets married you will not be able to sponsor her at all until you become a citizen.
They can't deny you a visa for not bringing her with. The instructions specifically say you must list all children under 21 but that they do not have to immigrate.

Sounds like a bug with the webpage. Choosing business should be fine.
Are you using High School or Work Experience to qualify?

Yes. There is no standard proof of finances but one of the requirements of the visa is that you won't become a public charge, so anything you have to show that is useful. They may or may not ask for it but better safe than sorry.

Hi guys
I’m a DV winner and hope every one of you has the chance to be
Is it necessary or even positive to bring some documents to my interview which shows that I have money support (bank deposits, house, and car) in my current country of residency?

Pick a city... just to let you know, San Francisco, Los Angeles, and New York are very expensive!
A friend of mine won the DV lottery and first came to Houston, Texas.
Once you get there, you can establish a P.O. Box to receive mail. Someone mentioned Craiglist... that's a great place to find a room for rent.
What country are you from, by the way? Maybe you can pick a city where there is a network of people from your country that can help you out in terms of finding housing, jobs, etc.

No !You can sponsor your self if you have enough funds to show at the interview ( assets, bank statments...)
And Not all the embassies require an affidavit of support!
And regarding the physical adress its a must if you succeed at your interview,because they will ship your GC to it !

Congrats on winning the lotto.
Now comes the time where you start shopping for your ticket and off to American soil you come.
Housing, well you could look at craigslist and see if anyone is offering a room and/or board for the price that you can afford, they also have jobs on that site as well. before you come here I would advise that you start getting an idea as to where you are going and what they have in that area. Dont wait til you get here to start looking cause you will be disappointed. Try to connect with other members of the forum or an organization.
I hope all works out for you