If the lender gets a title policy, what exactly is the buyer's one covering?

They're insuring two different people against loss, and the losses aren't the same size.

The loan policy protects the lender's lien position, up to the loan balance. If a long lost heir shows up with a claim to the property, the lender's exposure is limited to getting paid back what it's owed. Once the loan is satisfied that policy is done. The owner's policy protects the buyer's equity in the property, up to the purchase price, and it stays in force for as long as he owns it. In the heir example the lender gets made whole on $200k of loan and your friend, with no owner's policy, is out his down payment and every dollar of appreciation. Same defect, two very different numbers.

On the second question, who picks the title company is set by custom and by contract, and it varies a lot by state, with some states doing closings through attorneys instead of escrow companies. The seller's agent suggesting one is normal. Your friend can ask for a different one, and there are federal rules limiting a seller from requiring the buyer to use a particular title insurer as a condition of sale in some situations, which is worth confirming with his own agent or attorney before he pushes.

The escrow officer isn't anyone's advocate. She holds funds and follows the written escrow instructions both sides signed. That's why the instructions matter more than the personality.

@marlow's split is the one that made it click for me too. The other thing to check on his statement is whether he's being quoted the simultaneous issue price on the loan policy, since the loan policy is usually a small flat add-on when both are written at the same closing. If the loan policy line looks like a full separate premium, ask why.