Hey Tom! first of all, welcome.
The K3 is a great camera, so are the K30, K50, K500, K5.... pretty much all of them
For sure it will be a nice upgrade to your bridge. What's nice with DSLR is the many different mode you get, how much control you have over the pictures you take. You're new, stick to the green mode, learn how the camera chooses the settings and then move on to other modes if you wish. The K3 is full pack of features but it is also very easy to use and to learn (all pentaxes are).
For the mounts, pentax currently only have two, the K mount for the K series camera and the Q mount for the Q series (I'm not sure if the name is Q but it doesn't matter).
The K mount has been around since the 70's if I'm not mistaken and EVERY K mount lens will work on the K3. But as technology progressed, the K mount evolved to include more option (K, then Kaf, Kaf2, Kaf3), think auto aperture, then auto focus, then SDM focus... So every lens will work but you might not get all the features on it. But any modern lenses by Pentax will have auto aperture and auto focus. I could elaborate on that if you wish but you should get the point.
A mounts are for Minolta (sony) cameras, but only some of them. Some other sony will use E mount. But you don't even have to think about it since you're getting a Pentax
Again, welcome