There are scattered hills here in the Dallas area, and you can do a lot of riding without really going over many hills. If you do that, then the HH100 may seem hilly. It IS flat compared to a lot of other rides.

I use the 32 mm Gatorskins on both my tandem and my Raleigh Sojourn. They are not flatproof, but seem reasonable. My Raleigh Sojourn came with 35mm Vittoria Randoneur tires on it, and I had practically no flats with those. The limit on tire size is usually your frame, not your rim.

On any flat, check what caused it, if you have a sticker through the tire, it wasn't rough roads.

10wheels first picture looks like unusually rough chipseal. The 4th picture looks more reasonable, but can't tell for sure. It's rougher when it's fresh, and they use different size rocks in different places. As it ages, the rocks work their way down in the asphalt and it gets smoother.