Learn French: Il y a des restaurants très sympas ici. - There are very nice restaurants here.

No, il y a is a fixed phrase. It means both "there is" and "there are." Even though a comes from the verb for "to have" (singular), you do not change it to plural when talking about multiple things. You say il y a un restaurant (there is a restaurant) and il y a des restaurants (there are restaurants).

Why do we need des before restaurants if the English sentence does not say "some"?

In French, you cannot usually leave a noun "naked"; it almost always needs an article (a little word like "the" or "a") in front of it. Des is the plural form of un or une. Even though we often just say "restaurants" in English, in French you must say des restaurants (literally "some restaurants").

Why is the word order restaurants très sympas instead of très sympas restaurants?

Unlike English, most descriptive words (adjectives) in French are placed directly after the noun they describe. So, instead of saying "very nice restaurants", the structure is "restaurants very nice".

Is sympas short for another word?