It's a gall. Probably caused by a fungus, but possibly by a small microscopic wasp, mite, or other critter. Really, its only a cosmetic problem. Overall, I think the general recommendation is to do nothing, because it won't really hurt the trees, and its kind of expensive and hard to spray a large tree. If you do want to attempt some control next year, you'll have to find out exactly what organism is causing it, and what the specific control method and timing is. Most likely, if its a fungus, you'll have to spray with a specific fungicide prior to bud break in the spring.

Possibly, if they are growing from the roots and not the trunk, and you got some of the roots, you might be able to pot them up and grow them on to plant out in the fall. It does look as though the further-out sprouts are coming up from roots. I would think you would have better luck potting them than planting them directly in the ground, as you can pay better attention to watering a pot, especially on in part-shade, than you can to a somewhat fragile baby in the ground. One reason you may be getting sprouts is that it looks as though the mulch is too deep, certainly too deep right next to the trunk. There should be a minimum of mulch (best is none) right next to the trunk, and the root flare, where the roots grow out from the trunk and the trunk gets thicker, should be visible at ground level - the tree should not look like a telephone pole where it meets the ground. While you are digging down to the origins of the sprouts, you might pull back and possibly thin out the mulch at the same time. The mulch in all areas under the tree should be no deeper than 4". In any case, try to get down to the very base of where the sprouts are growing from, whether root or trunk, and pull them off rather than just cutting them - they WILL resprout in abundance from being cut, but might not from being pulled off - if they do, it would be in ones or twos, not multiples.

I've grown them in the past. They can grow quite big although I think there are several varieties, not well documented. The ones I've grown do ok without support, but ramble a bit (branches droop down, then grow up again). They are like a smaller tomatillo plant, which I find definitely needs some support. I think I have a decent picture of what a patch of them look like in September from back in 2008. Now that I look at it, I think they really could have used some support. In the front are some pepper and eggplants for comparison. I found picking them to be quite a chore. I think that's where the high price comes from. It will take you a fair amount of effort to pick a pound! Chris Here is a link that might be useful:

I have a similar situation: I have a sucker below the graft on a 1-year pear that I planted last fall. (The pear is Clapp's favorite, the rootstock is dwarfing but I do not know what it is.) I am wondering if I can remove the sucker, root it with hormone, etc., to make a new rootstock, and then graft a cutting from the scion on to it sometime in the future to get a cloned tree with a similar growth habit?