Even though the place we live in now has GDO, I can't say I'm an expert. I believe you can buy replacement remotes and there possibly are universals, but this is not like a tv remote. It's supposed to be secure so you can't just use any remote with any door. I've read of crooks who have scanners that can wait for you to use your GDO and " capture " your code. Then wait for you to leave then can open the GDO with it. I'm not trying to scare you, just some FYI. All this time on this planet, many houses and garages and this is my first with a GDO.
Mine is a roll up door and the GDO is a screw drive. The motor is attached to long screw with a nut with an arm running in a track. All this stuff is made to be inside a garage, out of the weather. If it gets wet, corrosion or dirt on it,, it gums up the works and really bogs the motor down. If not properly set up and maintained I'm sure the whole thing will quit as it also has sensors that if it pulls to many amps it thinks there something in the way and either shuts down or reverses.
I hope for your sake the freebies are complete because there's eyes, stops, sensors and all kinds of hardware that if it's not there will be a pain to find and could possibly be expensive to replace.