I think your H1 status (H1-B?) is likely to be your biggest pitfall here (see later comments). Technically, the H1-B visa names the (single) company for which you are allowed to work in the US. Of course, your client is not in the USA so you may be in a grey area.
On the other issues:
- Yes, just prepare a typed invoice, with your name and address, and send it to the client. Be sure to declare it on your next 1040. You don't need to set up a DBA or company.
- As far as payment goes:
- do not give them your bank account details. That's just basic security.
- Instead, agree an exchange rate from a reputable source, and ask them to send you a cheque drawn on a US bank for the amount in US$, then just bank it.
- You do not (in fact, legally, can not) charge them VAT. You need to be registered with the relevant country's Customs and Excise department to do that.
- Similarly, you do not charge US/TX sales tax, unless you are registered as a taxable supplier.
As another poster said, you should have sorted this out beforehand, and had a contract to work to. If you have protected yourself with a time-limited demo, then your chances of getting paid are good.
At this point you are on the horns of a dilemna ... if you collect the money, you can't risk not declaring it on your tax return. And if you declare it on the tax return, and your visa precludes such work, you could be packing up to go home real soon now.
So I really suggest you do some research into the H1-B status thing. An hour or two with an immigration lawyer may cost you $500 -- but compare that to having your visa revoked. If the lawyer says "you can't do this" ... you may just have to forego the $6,000 and decide whether you deliver the product pro bono.
I've done a bit of googling and found statements (from self-identified immigration attorneys) that doing work for companies OUTSIDE the USA does not affect your H1-B status. You may still want to confirm this for yourself, but it makes things easier.
The other consideration is ... what does your sponsoring company in the USA think about this?