some of the suckers/sprouts I haven't trimmed

Patch of dry rot; i do not believe we have had the irrigation emitters on since we moved in because they seem set too close

Overall my assessment is the tree is generally healthy except for the root suckers and the rot section. It may be it's in soil that doesn't drain well or receive much amendment, and I suspect it was mostly surface watered rather than deep watered.

It's tough to photograph the full tree, it's in the West/North side yard. We recently removed some of the low hanging, head-knocking branches because the tree was like an octopus. It's about 12' tall and 8-10' wide, with the lowest branches at around 4'

It's wrapping up flowering:

One weird thing I've seen on it are these patches of little lumps. They are on the trunk and branches. Like a tumor growth or infection?

Base of trunk, opposite side from dry rot:

A large flattish one on the ground over a big suckering section of flat root:

In California trees do need supplemental irrigation in the summer since we get almost no rain from May through November. The irrigation needs to be out by the dripline, not the trunk. http://ipm.ucanr.edu/PMG/GARDEN/FRUIT/apples.html

Agreed on the irrigation, it's totally in a bad place and I'll move it before turning on the irrigation.

So I've done a little research, seems like the bumps things could either been crown root gall or burr knots. Or both! I do not know enough to be able to discern between the two, but either way there isn't much to be done.

But what about the dry rot section at the base? Should I scrape it all out and treat it somehow?