has the suction bottom been reworked so that it adheres securely to cabinet surfaces like granite?

Keep in mind, granite is porous, that's why you need to keep sealing it. Suction cups need a smooth non-porous surface to work. So, your issue may just be the microscopic fissures in the granite letting air into and releasing the cup.

It says that it Includes One Multi-Purpose Stainless Steel screen. Does this screen work for tomatoes? Also, what is the width of the C clamp? My countertop has a rounded edge and I am concerned that the clamp won't be large enough.

I have used mine many, many times and I am extremely happy with it.As stated, the suction cup does not work well for me either. I have rounded counter tops as well. I have a 18" X 12" scrap of quartz when we remodeled the kitchen. We put some glue feet on the bottom. A chopping block so to speak. I attach the unit to the block. I can than move it to where it is comfortable to use. Works extremely well for me and I am very happy with it. Cut my work by half at least!

It doesn't say how large the container is. Most are 2 quart. Is this one 2 quart?

I would say the size of the funnel is about 2 quarts but it is just meant to act as a funnel. You use a bowl of whatever size you wish to catch the skins, seeds and cores and a separate bowl to catch the pulp and juice. I just keep cranking until my bowls are full.