I'm not US resident, I own (100%) a Delaware LLC.
As the LLC will be a webhosting company, the LLC will buy/rent dedicated servers
from a company outside USA and resell web space to customers worldwide including
USA (except Delaware state).

1. What are the legal obligations for the LLC's foreign owner with IRS ? Will I
have to pay something and how to do that ? (administrative forms...)

2. What about taxes if I sell web space to customers from others US states ?
Do I have to register as an out-of-state entity in each US states ?

3. As there is no obligation for a LLC to have a bank account, can I use a
personal bank account ? If not, can you provide a list of US banks able to open
a corporate bank account with VISA/Mastercard card for a low fee ? (strict
minimum deposit...)

4. Is there a legal obligation for Delaware LLC to to keep an accountancy ?

Questions appear to be clear, clear answers are expected,
clarification requests are welcome !

go to http://www.valisinternational.com and folow the instructions to
get a US Bank Account with MasterCard.

You don't have to show up in person and you should already have
everything that is required of you lying around your house.  The only
thing you will likely have to leave your house for is the Bank
Reference.