Bicycle Mechanics - "Restoring" a Supercycle Gran Sport

I recently bought this bike for $20, and it was in working condition. I ride BMX most of the time, and know how to repair virtually everything on a BMX, so I'm not new to bikes, I just need some help with certain things. Also, I don't want to pour a bunch of money into this bike.

First of all, I accidentally crushed the threads on one of the cotter pins on the cranks. Should I buy new cotters or should I buy new square taper cranks? And if I get new cranks, how do I know what kind of spindle to get? (length, diameter, etc)

That's it for now, I'll be asking more questions as I continue working on this bike.

New cotters for sure. Anything else requires properly identifying your BB threading, width, and chainline for a decent chance of success.
I don't shy away from much, but that's the kind of situation where I'd haul the bike to the shop and have them do the trial-and-error fitting of parts.
Odds are, whatever I end up paying them in time, I'm saving on not having to pay for parts that won't fit.

The issue is that the only bike shop near me is in another town an hour away. Also, what size cotters should I get (9.5mm, 9mm, etc)? Or does that even matter? It seems to me that half a millimeter would be an unnoticeable difference.

Measure the old one. 0.5mm matters.

Is it realistically possible to measure half a millimeter?

Also, I recently discovered that the headset on this bike has loose ball bearings, and I lost a few of the balls. Can I replace these with caged (unsealed) bearings?

Perhaps it might be better for you to "discover" whatever else is wrong or missing regarding this bike.

That way members can consult not only on what really needs to be done, but whether or not simply buying a new bike is the better option to begin with.

=8-)

Well really, nothing was wrong with it. It was rideable right from the start. I just really don't like cottered cranks and unsealed bearings, so those are the things I want to change. The stem won't come out of the forks either, so I'm going to pick up some penetrating oil and spray some in there.

This bike is pretty old - I'm guessing 70's or 80's - so it should have a freewheel, not a cassette, right?

Easily. Get an inexpensive plastic micrometer, $20 or so, try an auto parts store. The dial markings will be for 0.1 mm.


Is it realistically possible to measure half a millimeter?

Also, I recently discovered that the headset on this bike has loose ball bearings, and I lost a few of the balls. Can I replace these with caged (unsealed) bearings?

No matter what I try I can't get the stem off. What else should I try? PB Blaster? Kano Aerokroil? Cutting the stem off?!

FIRST, make sure you are using the right procedure. Just Google "remove bicycle stem" - lots of resources.
SECOND. If you still can't remove it you need to tell us what you have done and what happened. We aren't there, so we don't know if the stem bolt is rusted or if you got it loosened but can't tap down the expander, or if the expander's down but the stem is "welded" to the fork column, etc.

No matter what I try I can't get the stem off. What else should I try? PB Blaster? Kano Aerokroil? Cutting the stem off?!

Start by listing what you have tried, compare it to the comprehensive list on Sheldon Brown. Then let us know what the stem is made out of (and post a few good pictures).

As far as having to cut out a stem, sure, I've done it before when nothing else worked. Now on a Supercycle, I would probably be parting it out at that point.

I should give you more details...

First of all, just because I only have a few posts on here, doesn't make me an noob. I ride BMX everyday and I'm very confident working on a bike.

Second, I bought this bike so I have something to ride when the weather is bad or when I just don't feel like riding my BMX. I probably won't get rid of it because it actually functions properly. I just want to paint it and I don't want to do that with the stem and forks on the bike.

Things I've done so far:
-Loosened the stem bolt part way, then hit it with a hammer
-Hit the bottom of the stem with a hammer
-Sprayed PB Blaster EVERYWHERE
-Twisting the handlebars while holding the front wheel/forks with my legs

First of all, nobody called you a noob. Second of all, BMX is a completely different animal when compared to a traditional bike. Sure, a lot of the parts are similar in concept, but are actually much different.

Things I've done so far:
-Loosened the stem bolt part way, then hit it with a hammer
Did the stem bolt descend on that, or did it remain in the same position?

If it descended and the stem still won't come out, then the stem is binding to the steerer tube by the small gap between the cylindrical pieces. Penetrating oil and/or violence is the cure. I've read about soaking in ammonia for removing seized(aluminium) seat posts so I assume it'd work on aluminium stems as well. Some people use coolant spray inside the seatpost to get them to break free. Cutting is an option. Takes some time and skill, but is doable.

If the bolt didn't descend there's two options:
1) you didn't hit it hard enough
2) your stem is bottomed out in the steerer tube. Steerers are often a little narrower closest to the fork crown, and if the expander wedge is fetching up against that internal shoulder, no amount of tapping the bolt will help. In which case it's back to violence and chemicals.


Things I've done so far:
-Hit the bottom of the stem with a hammer

Huh?
As in keeping the bike upright, then banging on basically the underside of the neck/handle bar clamp?
Or as in inserting something through the steerer tube from below and hammering on that?

I don't think you'd get particularly good power transfer from banging on the neck/bar clamp, but it's worth a shot.
Can't see much future for the through-the-steerer tube approach either, as you'll be applying force in the same direction as the stem is supposed to lock in. Might just work for breaking free a bottomed out stem.


Things I've done so far:
-Sprayed PB Blaster EVERYWHERE

The key to having ANY kind of success with penetrating oils is soak-and-wait. Capillary action isn't exactly lightning fast. And if the fit is tight enough, there's a limit to how well it'll ever work.


Things I've done so far:
-Twisting the handlebars while holding the front wheel/forks with my legs

Is it rock solid, or moving at all? If there's any movement, just keep at it.