There are consequences to gifts over 10k, but I don't know what they are.

When the kids want to transfer title back to the parent, is it consider gifting in the tax code?

new construction there is a mandatory 1 year warranty by the builder by code in most states.then we buy the 2 10 as a parting gift.. home warrenties that you buy after market I suspect would not cover this.. regardless I would push back on this issue.. 

Is it possible to gift the shares once purchased, or is there another vehicle they should explore?

Will a gift letter from the source help?

That is your gift to the tenant

Essentially you find a multi unit building, get FHA financing for the least down payment and while you live in one unit, other people pay you rent for the other(s).FHA offers financing for up to 4 unit buildings, allows seller contribution toward closing costs and gift funds toward down payment. 

Make sure, for example, that the grandmother did not leave it to your client with your client's mother having only a life estate, or that the property was not gifted to the client rather than inherited.

IF you aren't living there I believe the answer is no, any contributions would need to be a gift. 

You can get gift funds from a family member to help you qualify - I always recommend using a low down payment option for any owner occupied purchase.