claiming of input credit

In case A the proprietor can transfer the credit to partnership. You have not mentioned as to whether it's partly used for proprietary use as well. So in the absence of part use, the proprietary concern if transferred as a going concern, then the partnership can take remaining credit for remaining useful life of asset. please refer to relevant rules on ITC in this regard. However, if not transferred as a going concern and simply the asset is transferred there without use by proprietor it will not be prudent for the proprietor to take credit.

In case B, yes if machinery is rented out, credit can be taken fully.

But please refer to the notification stating rates for renting out. If in the notification it has been stated that there is no ITC for such machinery then ITC should not be taken. So please be clear for what machine you are taking credit and the notification stating rates.