Hi!
1. You can use a single search, and translate all of the displayed texts (placeholder etc..) via the WPML String translations plugin. You can read the instructions here.
2. I’m not sure if WPML has multiple taxonomy term IDs for translated taxonomies to be honest. If you switch the language on the taxonomy editor screen, does it show different IDs? If yes, then you should be able to exclude them as well. But I am 99% sure, that WPML does not use different IDs for translated taxonomy terms.