Just to clarify, the lender does not reject an appraisal. Here's what happens, the lender (you pay for it) procures an appraisal to be done on a property to advise the underwriter whether or no that property is worth the price you've agreed to pay, thus informing the underwriter on the loan whether or not it's a safe risk for them to lend you the money. The more money the buyer is putting down, the less the lender will exert their control over whether or not the buyer may or may not move forward with the purchase if the appraisal comes in under what the agreed purchase price is. If it's an FHA loan, it's government backed, therefore they have the right to exert a fair amount of control. If it's CONVENTIONAL and the buyer is putting down 20% or more, the lender may allow the deal to go through because they have less skin in the game. Make sense?
So the lender is not rejecting the appraisal, they are making a decision to approve or reject a loan based on what the appraiser says is the market value of the property. Every property is worth something. The out of date stuff would only possibly make the property appraise at a different price than what is agreed upon in the purchase agreement. There are ways to make adjustments for that.
The lender is most likely reselling the loan to a 3rd party (Fannie, Freddie) and the house has to either be in a certain level of condition or be brought up to a safe and livable standard as a condition of giving the loan. If the furnace and electrical are all in safe operating order than I'd be surprised to see an issue from the underwriter but arguments can be made that the age of these items makes them high-risk.
A Renovation Loan can be used to overcome these issues by rolling the costs to make needed repairs into the loan itself.
Yes, a lender can.
Most lenders will "look out" for the buyer to buy a house in low livevable conditions without way to be fixed by the buyer because of low reserves.
Please, let us know what kind of financing you have.
First the finance is approved to you, then property needs to be sustancial accepted by the lender. There is no abligation for the lender to mortgage any property. As you know know, property conditons is an issue, clouds on title will be an issue too.
We, profesionals, need more information than two lines to give a better answer or we are all guessing.