During the 5 year look back, would Medicaid classify money my MIL contributes towards us for keeping and caring for her as a "gift"?

Another idea, find a bank that places copies of cancelled checks onto the Bank Statement. Gone are the days when one got the actually cancelled checks back.... [sigh]. But copies of checks would be very helpful to show where Mom's money was going.

Or you can make a copy of the invoice that Mom needs to pay and on that invoice place the check she or you had written. Thus, all on one sheet of paper.

I use to keep all of my parent's invoices in a 3-ring binder.

Well she must have some sort of income, surely? What's she been living on?

Yes, help her open a good basic bank account. Her money goes into that, and her income - pension, social security if she's eligible, whatever - is also paid direct into it. Then you can demonstrate exactly what she is contributing to the household, and what for; and you can keep records of what the rest of her money goes on. If it doesn't show on her bank statement, it will on the receipts. And you can get a basic little account book to record dates and amounts, which will be helpful to MIL anyway.

My mother in law has a little savings in a credit union and only just thought to myself she would have no check book neither a card which provides no proof of the money she is withdrawning from her account to whom it is getting paid to and for what purpose.

It could be a paying for something she is in need of, but as there is no bank statement stating who the money was paid to you have no proof and within the 5 year look back they may take it all as gifts !

So may be wise to put her little savings in a bank account for records !

What is your opinion and thoughts ?

Not the living expenses part, no. It's costing her something to live independently; just the same, it will quite legitimately cost her a fair, broadly pro rata share of the household expenses to live in your home. Or you can figure out what she'll add to the budget and charge her that. Medicaid don't expect anyone to live for free.

Her personal expenses - clothing, toiletries, perhaps her own cell phone and tv - you keep accounted for separately.

The care costs are a little different. If you or your wife or other family members need to be compensated for taking time off work to provide care or supervision, there must be a formal agreement with your MIL in place beforehand. The rules about family members being "paid" vary from state to state I believe? - so it might be best to get specific professional advice on that.

Hired care - professional in-home aides, overnight sitters, respite breaks - your mother pays for. Caregivers often feel odd about this, as though the help is being bought in for them; but it isn't. Anything that is paid for solely on your mother's account and for her benefit is a legitimate living expense of hers.

Even if your MIL is still in good shape mentally, this is the time to get POA and health care proxy documents sorted out. Don't leave it until you need to do it, because you'll miss the boat.
Always keep complete accounts, including statements, copies of bills and receipts.
Always bank her money and income completely separately from yours or the household's.
If in doubt, you can always call Medicaid and check with them.

I have one question, too. Are you all absolutely sure this is the best plan for you, your wife and your MIL? Do read around the subject and make certain you know what you're all letting yourselves in for.