- You're in a high-wind and/or earthquake zone (the heavy stud tie to the left is a clue).
- A small screwdriver will dig into the wood.
Should I replace this bottom plate?
Should I replace the stud too
YES, absolutely
You may well need to replace more than just the red circled area. Not because other areas are damaged, but because of the "extra" building strength required by your locale.
I'm 100% in support of DIY, but you may want to at least call in an engineer and/or experienced contractor to get an idea of how much needs to be replaced and if any additional tie downs might be necessary due to the splices in the sill plate.
Additionally, since this is a 2-story, load bearing wall and it's the fire break between the garage and the rest of the house, you may want to consider paying a pro to take care of it. Again, though, at a minimum, get a professional, on-site inspection to find out what's going to be involved.
Do remember that if you choose to do this yourself, you'll probably want to build a temporary supporting wall for the second floor above. If there's a basement/crawlspace below (not a slab), you'll also want to build a temporary support directly below this temporary wall to ensure that all the loads are properly supported.