I’m 84, a retired engineer, farmer and long time blacksmith. You’re right, Liquid Wrench is good and can help a lot sometimes, it’s acid a fairly good rust-buster.
For stuck bolts that broke off, lay a washer over the exposed bolt, same size as the bolt. Use the wire feed at a good strong level, burn down into the bolt and get it connected to the washer, keep going and let it build up in the center, we need it HOT.
Let it cool to room temp’. If you can catch the washer with a vise-grip, try to wiggle, use the Liquid Wrench.
If you can’t catch it then weld a nut to the washer or even a ‘handle’ out of steel, some bar stock that gives some power, like a 3/16 X 1 or even 1/4 X one, or narrower is it’s a smaller bolt, let that cool to room temp’ and more Liquid Wrench, hammer a little, keep wiggling and trying.
I’ve used a 3/8 air impact also, this can rattle them loose pretty well, use reverse and forward, work it loose and out.
I’ve taken many broken head bolts out of engine blocks this way.