How many grooves are on a typical 45 rpm record?

Check the videos as there is an adjustment. Also check for slipping belts.

https://www.google.com/search?q=Rockola+Sybaris+473+Jukebox+isn%27t+playing+at+the+right+speed

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Your terminology confuses.

Point 1. Why to you say, "Stuck?" Does it not make sense as a possiblity that the designers sought to prevent rotaton speed from being changed mid playback, especially on, say, an LP (long play) album with different side (stereo instead of 45 monaural) grooving. What would be the imperative of changing record speed in that manner...only one record type will play at a time. If changer, only one type record seriies can be played, all at the same speed.

Point 2. ...about "pitch...wildly out by about +7.

First, what are you meaning by pitch and by + (not -) 7. Since there is, to my knowlege, no record spin criterion known as pitch, are you referring to spin speed; hence to playback sound frequency, whether steady state or variable? If there is no user control of platter rotation speed on your unitn there would be little you can do other than to ensure all parts above and below platter are running smoothly with no drag or interference...possibly even lightening the record load on the platter, if a changer; and making sure records are clean to prevent slippage by washing with water or soap and water and air drying--avoid label. If your turntable is optically speed controlled (by timing marks on platter rim) those are typically adjustable to hasten or slow platter speed and therefore playback frequency pitch to your liking. "Wild variation" could reflect mechanical impedance as indicated above. Also check for record warping by trying known true record playback. Finallly, wild variation could be indicator of platter motor end of life cycle. Start pricing a motor if nothing helps.

I still don't follow the significance of the speculative(?) 7. Please explain if possible.

It thinks it's a 45 rpm. There is a trip lever near the edge of a 33rpm record on the turntable that may not be working properly.

I think you mean 45 rpm?
It sounds like you have got the belt in the wrong position. Try adjusting the position of the belt by experiment. Or you could look up the correct way to set up the belt.

There IS a silicon ring that fits in a groove on the bottom of the freezing bowl. I lost the one on mine, which causes the leaking described. I replaced it with a silicon O-ring (1" inner diameter, 1 1/4" outer diameter, ring thickness 1/8") that I found on Amazon - did have to buy a set with lots of different sizes but now I have extras in case I lose it again. Works perfectly without leaking.

The only thing (I think) that would cause a 45 to play badly and the 33 not, is either the cartridge or stylus, most likely the stylus. It's either worn or damaged, so it fits badly in the larger grooves of 45's then the smaller ones of 33!
The signal coming from the cartridge is the same on 45 as it would be from 33.

I am aware of jukebox mechanisms that would clamp down on the record, and if it detected a small-hole in the 7" disk, it would change the RPM to 33 1/3, and the large hole would mean 45 RPM.

However, if we drill down into the history of the development of the 45, we can see that it was developed as a replacement for the 10" 78 RPM disk. It was also intended to be played on a distinct 45 RPM player, and thus the large hole to discourage use on regular turntables.

Most of the 45s in the UK had a pushout centre (some round, some triangular). 33s didn't have this. Ex-jukebox records had the pushout pushed out, and clip-in new centres could be fitted

There should be a record size selector switch somewhere. It will move the arm to the positions for 12inch 7inch and 10inch records. It must be set to 7inch or 10 at the moment. For 33 it should be on '12' and for 45 on '7'.

ya buy new belt loose or is this direct drive