What, precisely, can be claimed as a tax deduction when you buy a home?
This is really a question you should ask a local CPA or whoever does your taxes. We encourage you to follow up with a professional tax advisor as we are not qualified or authorized to give advice in two areas - legal matters and tax matters.
Briefly put, providing you itemize deductions, own and occupy the home, you can deduct both property taxes paid on the home and interest paid on your mortgage. You can deduct the points and prepaid interest you make during the actual purchase, whether you pay them or the seller pays them on your behalf.
There are certain limits and restrictions which do not affect most people, but this is another reason you should contact a tax professional regarding your question.
New Construction: If a walk-through inspection reveals a problem, but I choose to go through with closing anyway, can I retain a percentage of the down payment (or mortgage amount) - - not to be paid until the repairs are made?
If you want to go through with closing, you will not be able to hold any of your money back or the lender will not fund the loan. You just have to trust that the builder will make the changes, and they normally do.