It's possible, I guess, that you may have shorted something out when changing the battery. Losing this array of functions suddenly isn't typical.
If it were me, I might replace the tail-light relay and see if this remedies some of the outages (several functions effected with this relay). If this turns out to be the case, you may then try to identify other relevant relays to test.
Also, just FYI, when checking fuses I’d recommend using a test light, rather than simply inspecting visually, as this also takes the integrity of contacts/pins into account.
Know this isn’t much help. Wish you luck.
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