You're going to want to think twice about mixing products because of the different shipping charges. Say you offer shipping at $5.99 for the first item and $1.99 for each additional item, like many of us. Then a customer comes along and orders a shirt, a mug, and a blanket. These will each have different suppliers, each with their own shipping charges. So you pay $4.75 for the shirt printer to ship the shirt, then say another $4.75 to the mug company to ship, and then a few dollars more for the blanket place to ship that (IDK shipping prices beyond shirts). You could easily have $15+ in shipping charges, but only have taken in $10 on shipping charges to the customer. That's going to seriously chomp into your margins, and depending on your margins you could even lose money. Better to have the apparel that goes together in one shop, and other goods in their own shops.

There are a lot of stores selling .pngs. That's one type of digital store. Lots of other types: planners, coloring pages, wall art, wedding invitations, etc. As to whether or not you should, that's up to you. But why do they want to buy the design? Do they want to print it on shirts? Just for themselves? On their own Etsy shop? Or some other purpose?