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.

Most likely yes, they would show up at the interview. Since you will be telling the truth on all of your applications, it should not be an issue.

Absolutely, you should feel free to do this. There is no way to know if the judge will agree but if you provide documentary evidence, your chances...

If your wife is not working, then her income is indeed zero. What you should do depends on who is filing for adjustment of status, and based on what.