What if I overstayed my visa?

Need more facts to answer this question. Generally it is possible but also depends if you are subject to a 2 year requirement to return home from your J1. Consult an attorney.

Yes, absolutely, it is possible, but ONLY IF you are not subject to the 2 year home residency requirement. (Even if you are subject to the 2 year FRR, it's not a tragedy, you can easily obtain a waiver, but must do so first.) If you are not, then kindly note that spouses of USC's are deemed to be "immediate relatives" and as such are not even expected to maintain status. You will be able to adjust status anytime you want (but of course, the sooner the better) and will not be penalized for either having fallen out of status or having worked without being authorized to do so.

Yes it is. However, if you are subject to the two-year home residency requirement, you will need a waiver.