Yes, more or less, and Yes.
99% of the PTO's are 540 RPM, and standardized, with big chunky splines.
Some tractors will have a 1000 RPM PTO which can be a couple of different sizes, generally with smaller splines.
I think my Wheel Horse D200 Garden tractor has a 1000 RPM PTO with some kind of an odd female small splined connector, so watch out for some of the garden tractors.
Also, keep in mind that your PTO must slide back and forth on the shaft which is generally made in 2 parts. These two part shafts are specific to the implement. While the tractor couplings are standardized, these shafts ARE NOT standardized.
The size of the 3 point hitch is generally dependent on the HP rating of the tractor. A good summary is here:
TractorData.com - Three-Point Hitch
You'll find the Category 1 hitches in the smaller 20 hp range tractors, and the Category 2 hitches in the 50 HP range tractors. The larger hitches are both wider, and have larger pins.
Some implements such as my rake are configured to take either Category 1 or Category 2 hitches by having inward facing category 1 pins, and outward facing category 2 pins.
International Harvester came up with a uniquie 2 Point "Fast Hitch" which you may find on some of the older IH tractors.