How can we get the ice hold released.

If you have evidence of his being a US citizen let ICE know. If not contact an immigration attorney.

Can I apply to permanent residency via my employer after divorce?

You must maintain status if proceeding through your employer. Discuss with your employer's immigration attorney.

If I let my EAD expire, do I now renew or apply as a new candidate?

As my colleagues have noted renewal follow instructions for the application.

Do i need a divorce lawyer or do i need a immigration lawyer

Both - divorce attorney to end marriage, immigration attorney to retain resident status.

Can I use my renewed Ukrainian passport to re-enter to US?

Not recommend, better to file for and use a refugee travel document.

I am green card holder(not citizen).How my future wife can file a family-based immigration petition to apply for her green card?

As a resident after marriage you may file a visa petition I130) for your spouse. There is a wait due to priority dates. You can upgrade the...

What do I have to file paper wise to leave the country after the divorce? Can i still enter U.S. for travel?

To surrender your resident status file form I- 407. After surrender you may apply for visitor status.

Can I go for Visa stamping with Employer B when I already have Visa stamp with Employer A.

If employer B petition is approved, you should be able to apply for visa based on employerB. Before filing check with employer B's immigration...

This not a US Immgration law question. You may want to repost your question on a another thread.

What would be my current status now as my COS got approved on March 18th but approval notice says its valid from June 1st.?

To be considered in H1b status you must be employed withe the H1b employer. Your H - 4 starts the day of authorized approval.