No, specifically dim sim, rhymes with Jim. Dim sum I’d wager some people would think you’re mispronouncing dim sim, and others would understand it to be dim sum (which we generalise as ‘what you eat at yum cha’).

Yes there are vegan ones but they wouldn’t be commonly sold at fast food stores. Dim sim are commonly found at fish and chip shops and are an accompaniment to that meal, or standalone snack. If you wanted vegan ones your best bet is finding frozen ones at the supermarket.