How does this attach to the toilet? My mother has similar that doesn't attach. It tips as she rises. She puts wait on one side to transfer the sink.

The toilet seat riser sits above the toilet bowl lid. No attaching is required.

Is this seat good for men who have to sit to wee? Is the "hole" big enough for everything to fit down in...? Is it big enough to wipe easily?

In my opinion, the only benefit of this seat is that it has high and sturdy arms. if you have difficulty rising to a standing position from sitting, this is a handy device. Otherwise, it has a lot of issues. The seat hole is too small and the seat itself is not well supported. The "funnel" under the seat, which bridges the seat to the opening in your toilet is a separate piece that is screwed to the bottom of the toilet seat. It should be one piece with the seat or at least there should be a gasket between the seat and funnel. If one doesn't aim totally down, one may find liquid dripping from between the two pieces. The two arms are attached very closely to the sides of the seat making wiping or even changing alignment with the hole challenging. I am 5'7" and 165 lbs., anyone much bigger than I will find this seat too tight. Also, I would recommend sitting down carefully as too much bouncing will probably cause the screws attaching the seat to the legs to break out of their plastic holes, dropping them in the toilet and setting-up the occupier for an interesting ride.

does this sit on top of already on there toilet seat and is the splash guard removable for cleaning it?

Yes, it sits on top of the toilet seat in your bathroom. The splash guard isn't meant to be removed because it is connected to the bottom of the plastic toilet seat.

Can it topple over? The person uses his fists to push himself up.

If someone uses all their weight to steady themselves on one side, it will topple over. My mom has done it once. I still like the chair, I just have to monitor her when getting on it.