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Most RV manufactures use some version of EPDM roofing materials (rubber), and also versions of the TPO roofing materials (thermo plastic compounds)...., yours appears to be a version of the EPDM materials.
The best solution for the tear is a product called Eternabond Sealer Tape, comes in different widths but 4" seams to be the most common used by folks with RV's. Check for any moisture damage do the the exposed wood structure.
I wouldn't be surprised that your roofing material is starting to break-down do to age....., may want to consider replacement if you plan to keep the FW for a number of years.
There are numerous roofing seal-coat products on the market for RV roofs (I'm not a fan of), you may want to consult the prior owner on which one he used, this information will lead you to how to remove (if possible) and/or if anything can be applied on top of it.