Welcome to the forum.
Eternabond is an excellent choice for covering the roof seams.
Another option is
Dicor Self Leveling Lap Sealant.
Use Dicor non-leveling for the side walls. Shop around for the best price.
I would use the Eternabond. It's a one time repair.
The dark sealant on your roof could be silicone, which is not a good choice for a RV.
I would remove as much as possible. Try a heat gun on low and a plastic scraper.
It's difficult to get something to stick to silicone, including more silicone.
Hopefully it's just a non-silicone type caulk.
If you really want to check for leaks, consider a
Pressure Test.
Enjoy your travels.