Hi - and welcome to the forum.

Q 1: Pretty much, yes. Like Synthia said, you can always try getting a transfer within your current job. But any visa you get that way will be tied to that employer/employment. Lose the job - and you lose the visa (and have 30 days to move back home).

Q 2: I've seen websites that offer job listings for those looking for sponsorship, but I'd be wary of them. For starters, they are expensive and no one can guarantee that you'll get a job that way.

The best way to get sponsorship is to work up a dynamite resumé that highlights what skills and experience you have that is lacking (or seriously ununusual) in the US. Then research companies that need those skills. Could be languages for countries where the company wants to expand, could be business experience in a part of the world where the company has ambitions.

It's not a bad idea to target larger companies. Smaller ones don't generally need the exotic skills, and aren't so keen to get into the hassle and expense of "petitioning" for a foreign worker. It's also better to shoot for international companies, as they have more experience with hiring and transferring from overseas.

Job hunting in the US is considered a type of marketing. You have to market yourself - show them why they should sponsor you. And it helps to convince them that you already know lots about the company and what you can do for them.
Cheers,
Bev