1. Are you saying that the accommodation is, your DC may type not only long assignments but short answers too? Are you saying you want the teacher to give your DC a chance to re-do the assignment with typed answers? OP only you know how critical the assignment was, for learning or grades. We can't know. It's almost the end of the quarter. Go ahead and send a short email if it's important enough.
2. Yes, appropriate to ask for an alternative. The weird thing about this one is that word searches don't measure any curriculum-related skills. So in theory, there's no accommodation needed. An alternative could be for your child to type out a list of the vocabulary words the teacher on the word search (?).
3. Do you think that the space provided is impacting your DC's math test answers? Then make your case and get buy in from everyone. It can be added to the 504 or done informally. One option is to send your kid in with graphing paper for them to write on and attach to the test. Graphing paper helps many math students keep their work on track, and can be helpful for students with dysgraphia.