She's a baby who doesn't really know how the world works yet. Most puppies don't even really know how to understand and respect other dogs' body language yet, nor do they always have the self control to back off when they should. Cats are basically speaking a different language than dogs, so it's going to be even more difficult for her to understand what they're trying to tell her, especially if they do things that dogs can interpret easily as play, like running away or smacking her with their paws. You need to reinforce the cats' "leave me alone" signals by stepping in and removing her when they tell her to back off, and preferably before they get to the point before they're really upset or running away. It may well be best to separate them completely except for supervised interactions during calm periods until they understand each other better and she's mature enough to have more self control.
As for the pottying issues, is there a reason you need to use potty pads? I find that teaching a dog to potty on a potty pad often leads to confusion about whether it's okay to potty indoors, and in many cases even confusion over why rugs, bath mats, a stray shirt, or any other absorbent, pad-like object on the floor are different from their pads. My first dog was potty-pad trained when he came to us at ~12 weeks, and would seek out pretty much anything pad-like to do his business on for ages before we got him properly housebroken.
When and where does she poop? Does she seem to be a 'shy' pooper and want to do it where you can't see her? Sometimes this happens because a dog's been scolded or even hit for pooping inside, and they learn not that it's bad to poop inside, but that it's bad to poop in front of humans. Sometimes a dog is just weird. You may have more success with her pooping outside if you use a longer line so she can get some distance and/or go behind a tree/bush/etc. to do her business. If she poops in front of you no problem, just in the wrong spot, wait her out. Bring her somewhere boring and just hang out. Many puppies get overwhelmed and distracted by their environment and totally forget they have to potty at all, so it takes way longer than it seems like it should. After you manage to wait her out and throw a treat party for a successful outside poop a few times, she'll be much more motivated to get her business done quickly for that sweet reward.
For both the potty issues and the destructive behavior, she needs to have a puppy-safe area where she can be when you cannot supervise, even if it's two minutes while you run to the bathroom. This can be a crate, pen, or room, but the general idea is there's nothing in this space the dog should not have unsupervised access to, just appropriate toys and chews. Crates are often the easiest tool to assist with potty training, because most puppies won't want to potty somewhere they'll have to lie in the mess, so they'll be encouraged to hold it (though remember they're still babies and physically can't hold it very long). I use pens, which gives a dog a little more freedom to move around and interact appropriately with chews/toys and learn how to entertain themselves. But in the end, it really just depends on what works for you and the space you have in your home.