Is it permissible to sell by installments with an increase in price if I do not have a shop or merchandise, but rather I purchase the item in my name after the buyer requests it, knowing that banks do not own merchandise in their Murabaha dealings?

There is no objection to selling in the manner described, provided that the sales contract between you and the prospective buyer is not concluded before you purchase the item, take possession of it, and it comes under your responsibility. This is a form identical to Murabaha to the one who orders the purchase, and it has been permitted by contemporary scholars and jurisprudential councils.