I'm terribly sorry to hear about your loss. I am not aware of any U.S. immigration benefits you can get as a result of this, but rather I suggest...

If you got your TPS extended, you should have an EAD, that's all that they send, I have never gotten an approval notice that I can recall.

It takes 30 days to two years and anywhere in between. It is unpredictable how long it could take. Could be soon or could take a long time.

The H1b should not have any impact on your I-130 petition. Nor will entering the visa lottery have any impact.

If you have been living with your husband continuously as a permanent resident for the last three years, and for those three years he has been a...

No, a speeding ticket should not have any impact on any of your immigration applications for H1b or other status.

There is no harm trying. If you can convince the CIS officer you intend to leave the U.S. after six months you can be approved.

Very doubtful. You should contact a pro bono organization to hire them to help you with your detained relative. Or find a private attorney who...

You should write to your senator and congressman to complain about the USCIS being too slow in their processing times.

Getting permanent resident status, and not citizenship, in Mexico or any other country will not jeopardize your U.S. citizenship.