Yes, they can, if they touch the genitals, if they have oral sex without any barrier. In the case of blood-borne diseases, infection is possible if there are wounds or cuts on the hands. This is in a nutshell, but here is a whole article on this topic - lesbiru.com
Of course they can. Sexually transmitted diseases are transmitted not only sexually, but also by household means. You can get infected through dishes, toiletries and bath accessories, etc. I will cite one Soviet anecdote. In the pub at the table, two visitors are drinking beer. Both are squeezed out of the glass right behind the handle. One asks the other why you drink like that? In order not to get infected. And why you? In order not to infect.