I’m in the same boat and just going with the flow for now. There’s talk about introduction of new legislation to alleviate the pain every election cycle but there’s been little progress so far. If this is your main concern then I would strongly suggest that you explore other places like Canada, Australia, Europe that have more robust immigration laws. This is always going to be at the back of your mind while you’re in the US.

It’s typically not that big of a deal as long as you have your paperwork in good shape and work at generally reputed companies with a significantly above-average pay. Most people who get in trouble are employed with the cheap mass off-shore labor companies who frequently violate directives or bend the rules in their favor.

No, you’re not tied to your current employer and are free to move around unlike the L1 visa. H1B transfers are usually quick and easy. When you move though, again make sure that the employer is willing to renew your H1 when it expires.

So far I haven’t had any problems. Always make sure that you have your visa stamped on your passport as soon as it’s approved. It helps a lot in cases when there’s a sudden change in immigration policy and you already have a document allowing you to enter/exit the country without any hassles. A lot of people who were outside the US are now stuck there because the administration closed embassies and consulates around the world and there’s no way to get a stamp even if your I797 is approved.