Normally she cannot. If you showed exceptional circumstances caused you to file late, there is a chance.

You can try filing again and request that the application be accepted late due to exceptional circumstances.

Unless you applied for concurrent employment, you are no longer authorized to work for your first H1b employer.

Fiance visa is often faster than an immigrant visa.

You risk getting a denial if you do not file any response, so it's probably worth it.

If she is not in status, you should wait until you naturalize and then you can file for her and she can file to adjust her status.

Since both are available, it should make no difference.

There should be no unlawful presence during J1 grace period. There should be no problem traveling out of the US if you have advance parole.

No, you cannot enter on an H4 if your spouse is not an H1b.

It does seem that that is what it does mean.