The grout needs to be removed where the tub meets the wall and in the corners. That should be caulk. Old caulk needs removal. Silicone won't stick to cured silicone. Use a good silicone like GEII.
The floor. You can cut out the damaged portion and put in new subfloor. I would recommend something other than particle board.
They make plastic shields you can install to prevent water from going over the edge like that. Splash Guard https://www.amazon.com/Bathtub-Transparent-Adhesive-Bathroom-Restroom/dp/B09JSWYD1D/ref=sr_1_1_sspa
No, they aren't attractive, but are effective and in some cases, the best solution.