Are patented seeds of sweet seedless peppers from breedx.com GMO?

You as a consumer will not ever buy GMO seeds, accidentally or intentionally. Because the genome is a protected product, farms who buy GMO seeds from companies like Bayer (formerly Monsanto) have to enter into a legal agreement with the seed supplier, and they buy massive quantities at a time. Many public seed companies proudly declare their seeds are non-GMO, but that's true of all seeds you'd be purchasing.

The seedless plants that you as a consumer can buy are bred by creating a sterile hybrid between two non-sterile lineages. It's essentially a "defect" in the children of the two lineages which prevents their progeny from developing seeds even though they still develop fruit.

Edit to answer the rest of your questions:

Legal to use biological waste: Use freely.

How the patents work: Patented plants are basically just a legal protection for the company that produces the seeds you're buying. They've put a lot of work into generating lineages of pepper plants which can be cross-bred to produce seedless peppers, and their patent ensures that they are the only legal supplier of these plants (these specific plants--someone else could breed separate lineages and patent their plants without any issue). The USDA website and US Patent and Trademark Office website have more information, but I'll summarize: You could be sued if you bought their patented seeds, grew pepper plants from those seeds, then created a business to propagate and sell those pepper plants. You, at home, growing food for you and your family/friends? No one cares. The patent only exists to prevent another company from taking the plant that the original company painstakingly bred and selling it as their own.

Implications for society: You can't build a business selling their patented plants without a licensing agreement, I guess. Nothing odious about hybrids, and protecting specially-bred plants is enshrined in the Plant Patent Act of 1930, so it's been around a long long time.