Well, his bars are waaaay overgrown, and that's making weird ridges in his hind foot, and this is one time I would actually cut some out of the bottom of a foot, which is rare for me.. I don't see the lump on the frog that you are worried about, maybe it's the bar that you are looking at? The hard ridge next to the frog. And yes, it could cause a pressure point in his sole and make it bruise, so a good trim will take care of that, and it's unlikely that you would cause pain with a pick or brush, but body weight could make it tender. Fortunately, hind feet don't tend to get as sore since they usually pack most of the weight on the front end. The frog doesn't have any real flappy parts that I can see, so I would be tempted to leave as is (unless in person I find white, powdery funk, but I'm going by a single photo here).
Now the front foot, the frog has a flap at the apex just begging to be trimmed off (conservatively!) I would trim the heels a tad and clean up the quarters, but the toe..if you look at the sole next to the white line (I can copy and repost your pics with the area marked if you would like) you will see a bulge in the sole. That could be the coffin bone pushing down, or it could be toe callous trying to form, but from the picture it's hard to say. Either way, DO NOT TRIM that part of the sole!!!! Just trim the toe wall to slightly longer (or "higher") than that bulge and bevel the crap out of it. Again, from a single pic it's hard to know what we are looking at exactly. But my assumption is that's the coffin bone bulging, explaining why he's reluctant to pick up his feet.Looks like there might be a bruise at the end of the apex of the frog, but can't tell from here. I've seen this in a lot of horses that go too long without a trim and live on soft pasture. It's going to take some frequent trims to get those hooves back in shape, but is sure fixable, and after the first good trim, this horse will be much happier. The hind looks far worse than the front does.