I'd suggest a check rather than cash, and document well. you'll then be a preferred creditor of the estate.

Is there an inheritance tax if retirement account if rollover by the inheritor?

in NJ there's an inheritance tax if left to a non class A or Class E beneficiary with very few small dollar exceptions. I'm not aware of an...

Cut out of will and life estate....

I've said this to other posters. If you read your statement neutrally, you'll have answered your own question.

Will and life estate

Reread your post with a clear, unbiased mind, and then consider your chances.

Does the money from joint bank account (me and mom's) count as an asset of my mom's estate and need to be used to pay debts?

it is a non-probate asset, yet part of her taxable estate. it passes outside of the will, but can be attacked by creditors. A competent attorney...

Administration expenses such as the funeral are a priority

If my sister had a joint account with my recently deceased mother who died intestate, would she be entitled to the those funds?

By operation of law probably but there can be other factors.

My mother filed a couple lawsuits but passed away a month ago. Do those close since she's gone or 'pass on' to heirs/family?

The estate can continue the actions or even initiate new ones

Being POA; my mom is currently in a home pending medicaid. If accepted can medicaid take out a lien on my house to get payment?

it sounds to me like you are okay and safe, but there are a lot of moving parts here - you should consult with a qualified attorney right away to...

I co-purchested my home with my elder mother. 50/50. 4 years ago we put deed in my name. i live there can medicare claim it?

do you mean Medicare or Medicaid? there's a very big difference.