No, loan programs like FHA requires only 3.5% of purchase price as down payment, and conventional programs like Home Ready and Home Possible only require as little as 3% for down payment. There are even Down Payment Assistance Programs that will allow you, if qualified, to purchase with $0 down payment
Buyer and seller can agree to reduce purchase price to conform with appraisal value, the buyer can come up with the difference if no agreement to reduce, or the deal can be canceled if no agreement reached or buyer unwillingness to provide the difference.
Yes, there is a specific time during the transaction, usually after the inspection periods, during which buyer can ask seller for repairs. Seller will answer agreeing or not to all or some of the repairs, or crediting buyer some money instead. Everything is negotiable between buyer and seller.