1. Yes, I think you can keep that H-1B alive as long as that job is there.
2. Yes, as long as you have an H-1B approved in the last six years you can always transfer over to another employer and if your I-140 is approved for 180 days or more which in your case would be from June to December. So next year onwards you are entitled to have H-1 extensions through any employer as long as your I-140 remains unrevoked for 180 days. I don't see a problem you can have a transfer from India itself. More...
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