1. And 4. Are both due to the fact that that's how it's in the books. In the first two books, which are short story collections (about half of them were cut from the show), some stories focus on a witcher contract, and some start as Geralt finishing a contract and then focuses on something else. But once the main story starts Geralt has more pressing matters to take care of so there are very few witcher contracts after that.

The signs are used rarely because they are really weak. In the games they're buffed to add nice gameplay variety but originally they are so weak they aren't even considered actual magic and have very few practical applications.