Not any quicker than if you hadn't. However, your children will be citizens.
Your best bet is to get married in U.S make sure to get all proper documents,like visa passport and You'll be good to go!
No. You need your US passport.
You go to immigration and start the paper work.
Sure.
ONLY if you have your papers and proof that you are married with a citizen or resident, if not, you are considered an illegal in the U.S.
Yes. Easily. Especially being a UK citizen, it does not require the UK citizen to go to the US if needed for the immigration process.
A US citizen with a green card can get married to a Switzerland citizen if they have the proper documentation. To do so, you need to go to the office where all marriages are processed and they can tell you which documents specifically you will need.
There is no procedure. There are ways... get married to US Citizen, get company to sponser you and then apply for citizenship... sorry no procedure.
This depends of your country of origin; see the link: http://www.mae.ro/node/26966..
What card did you lose? Green card? If you were adopted by US citizens, you are already a US citizen, not merely a permanent resident. Getting married does nothing for improving your status. I'd go see an (immigration) attorney and order copies of your documentation. This shouldn't be too hard to get if you had them originally. Good luck.
go there and check the local courthouses
No, you will have to get divorced, you will almost certainly get sent to prison for bigamy.