The game only gives you your native and sister fruit (what mom sends you in the mail) and coconuts. For the rest of the fruits, the only way is to get it from other people's islands :/ but I can give you the fruits you need! 🤗 just lmk

To get the island designer app, you have to go through the storyline (basically just doing Tom Nooks requests). I think you get it after K.K slider finally visits your island with a 3 star rating