I'll try to help out as best as I can!
1. Bedding is really up to you. A lot of people love fleece, personally with a really old washer and dryer I don't want to end up burning them out by constantly washing large loads of pig bedding, so I use a disposable paper bedding instead. There are pros and cons to each, but pigs will be happy and comfortable on either. I don't recommend wood shavings, although they are cheaper than paper, because they don't absorb as well and the aroma can irritate the respiratory tract of many animals (and people- after years of small animals on wood chips in my youth, I am completely allergic to cedar/pine/aspen now!)
2. Pigs can't live on just vegetables. They will not wear their teeth down adequately or get enough long fiber in their diet. Veggies are treats. The most important thing you can give them is an unlimited supply of timothy hay. This gives them the fiber they need, wears their teeth, and is the single most important food item. I also give a vitamin C fortified pellet daily. Guinea pigs, like humans, do not make their own vitamin C and can get scurvy if they don't get enough in their diet. I also give fresh foods with vitamin C, but the pellets are a good failsafe for when they do not get as much vitamin C from their daily treats.
3. Floor time. It's really up to you when you can work it in. If you can block off an area or buy a large pen, it's possible to give your pigs floor time without you being right next to them supervising at all times. Mine are in a hallways where I block off both ends and give them floor time with treats to forage for nightly. I can see them from where I am sitting on the couch.
4. I don't personally have larger pets, so will not be much help there. Some cats have more of a prey drive than others (my friend's cat used to kill rabbits in their yard- he would easily have killed something the size of a guinea pig. My other friend's cat sniffs at the pigs, but is actually freaked out when they move and runs away from them.) Some guinea pigs will learn to tolerate other animals and others will be terrified. For safety, personally I would not leave a cat in a room with a guinea pig that was not fully enclosed unless you are supervising them- so I wouldn't use a cage that wasn't covered on top and would keep the cat out or watch really closely during floor time.