Another picture.

Sorry, this is the tumor...

Moss?

The split appears to be sun damage. Does it face west or south/west? Perhaps someone with a bit more knowledge can confirm or deny.

Not moss. Lichen.

I have to say that tree doesn't look promising at all.

The tumor looking things could be Black Knot.If it is,about the only way is to physically remove them.It can get serious.There was some on a Plum of mine and I was able to cut and scrape the area,but if possible,cut the branch off.I couldn't,because the growth was right at a junction on a multi-grafted tree.
It seems like the previous owner didn't take much care with your Plum tree. Brady

Yes, it looks like Black Knot. I had a plum tree with it. After a few years of continued decline, I had to have it removed.
There's lots of articles about it. I've linked to one basic description of the disease.

Here is a link that might be useful: Black Knot Disease

Black knot can be managed with most varieties-most sites if one is diligent about removal of galls. The right knife is helpful- I use a CRKT "Thunderbolt 2" which you may be able to find on-line. Some times a hand pruner and even a pruning saw are also essential when the gall gets hard.

You need to cut about a half inch beyond the gall parallel to the branch or trunk and as far beyond and behind it as necessary to reach clean wood (the infection moves up and down with the vascular system, not so much sideways). Cut right through all the soft cambium and bark to hard wood.

Collect and bury or dispose of removed bark and wood.

I spray the "surgical" wounds with chlorathalinal- one of the few fungicides that even has a shred of efficacy against the fungus.

Thanks everyone for all the info. Im gonna try and save this tree, though it dosnt look too good right now.