Prop shaft came loose

Out of the hole, the engine revved and there was no forward motion. Shaft did not break, it just slipped out of the coupling. Now I need to put it back but I have some questions.

There are indentions where the two coupling screws were just pressed into the side of the shaft. And when I felt in the inside of the coupling, none of either shaft screw extended into the coupling, so I assume they were sheared off.

Should one of the these screws have been in the keyway? If so, what does the screw look like and where can I get a replacement? Also, why are there two screws?

The coupling is shot if the shaft fell out. The alignment is also suspect since the shaft fell out.

The alignment was good. Prop turned easily by hand.
What is the keyway for if the coupling had a keyway too? Does it have the male version of the keyway for the shaft to slide onto?

My brother in law explained the key to me. (For anyone searching, the key is a square shaped rod that fits in the grooves of the shaft and the coupling.) Found half of the broken key in the back. I took apart the coupling and it looks good. Shaft looks good except screws were broken off. Are replacement screws a common enough item?

The key most likely handles little of the torque, the zero clearance fit does that. In forward the shaft is trying to push a hole though the engine so it has to get pretty wallowed out for it to fall out the back.

Merritt - You will need to measure both the shaft OD & the coupler ID to determine if these parts can be reused. Take 3 measurements (120 deg apart) with a micrometer on the shaft OD, then average them.   Likewise for the ID of the coupler, except you need an internal mic.   A machine shop can help you measure these if you don't have access to the gages.   You need the shaft average to be .001 inch bigger than the coupler ID average (press fit).

Well, last time I checked the alignment I used the gauges suggested here and it was aligned perfectly. I wasn't going off of just the turning by hand.
No, I don't have the tools to measure the ID and OD of the coupling and shaft.
All the marinas were closed today but I'll have someone look at it in the morning for suggestions.

Also pictures of events like this are worth a thousand words.
If you can post some pics of the shaft and coupler it would help with the diagnosis. You maybe wasteing your time and money trying to put it back together.

I have pics but need a web guru to give me permission to post.

You don't actually need live approval you just aren't doing it correct.

New coupling same shaft. Idle speed it was smooth but when under mild speed it is pretty rough.
I didn't have my gauges with me to align it. Got the gauges from home and I will do a thorough alignment tomorrow morning; weather permitting. Anything else I need to check?

It was a 1inch coupling. Shaft is not egg shaped. Flat front with keyway. Coupling has two set screws. Each 120 degrees around from keyway. Not heat fit.

get ready... here it comes...

wow, post on here asking for help, get help, ignor help and do exactly what told not to do.

you can lead a horse to water...

Look guys, I apologize. I'm a school teacher with three kids who like to ski. I am not a mechanic. Nor do I have loads of money to spend on one.
In the past you guys have helped me replace the steering cable, fix an overheating engine, rebuild a carburetor, align a shaft prop, decide how to handle a broken fuel gauge, give suggestions on towers versus extended pylons, and how to fix several routine issues with a thirty-five year old boat; and I thank you all. Everybody usually responds in a matter of minutes instead of days and have been patient with my amateur attempts sometimes explaining things in plain language I can understand.
I usually get access to a lake house for two weeks a year and spend half the time keeping the boat running. I'm not complaining because I love getting out of the classroom and getting my hands dirty rather than just doing the easy thing of selling a classic Ski Nautique and buying some stupid plastic boat like the Seadoos and Sunbirds others buy.(I think you guys know what I mean.)
I have very limited assets and can't just shell out hundreds of dollars every time I go out on the water.
In previous years I have had plenty of help from the experts here.
I normally search every forum post first so I don't ask questions already explained elsewhere.
So, please, if you are willing to explain to me what I should do and how to do it like most of the Grand Poobahs have done in the past then I appreciate the help. I need it in simple language to a guy who has never messed with a shaft before.
However, if you feel the desire to answer with "you're just doing it wrong" or "you can lead a horse to water" or some other unhelpful condescending response then please stay out of the way and let the guys who are willing to take their valuable time and actually help me to understand do the replying.
I'm doing the best I can with what I have.
Now,
I took the coupling to a veteran boat mechanic and machinist. He told me where to go to get the right coupling. I got a coupling made for a Ski Nautique identical to the one I took off. I don't know what it means to be heat shrunk. Is a heat shrunk coupling different than the coupling I took off or is it a process for mounting the new coupling?
I want to do it right if I can.
Do I need to remove the prop and shaft completely in order to fasten it to the coupling or can the coupling be replaced without removing the shaft?
What length square rod key do I use and how do you properly seat it in the coupling and shaft simultaneously?
These are the things I need help in understanding.
Call me whatever insult you want, I guarantee it's not worse than what my elementary students have called me. But if you are the patient mentor type, willing to help a newbie amateur, then you are acting like the true professionals who have helped me in the past. Thank you. You are the men I have grown to truly respect and come to for help.