Verified answer

"There are six restaurants." = Resutoran ga rokken arimasu.

Note: -ken as in "rokken" (comes from "roku-ken") is a counter for restaruants.

"There are restaurants that sell Mexican food, Chinese food, pizza, and donuts." = Mekishiko ryōri-ya to Chūka ryōri-ya to piza-ya to dōnatsu-ya ga arimasu.

Note: The suffix "-ya" means "shop"; when preceded by a food name it can also mean "restaurant". This means that each of those restaurants is specialized in one of those foods; if you mean all those restaurants sell all those foods, could you tell me so in Additional Details.

"There is a school close to my home. The school name is Trident." = Watashi no ie no chikaku ni gakkō ga arimasu. Gakkō-mei wa Toraidento desu.

Note: "Toraidento" is how we phonetically render "Trident".

　ビーザやちゅうごくのレストランがあります。 This ya means that pizza and japanese food are examples of the types of restaurants. describe those first, then use そして, メクシこりようりのレストランもあります。 shite is an 'also' form, and mo is adding to the previous statement. These are all in the first beginner text book i used, so they should be acceptable.

わたしのうちのちかくに，こうこうのなまえは『トライーデント』です。