They're great fun. I'm no expert. I have a Bambu Labs A1 at the moment but am upgrading to a bigger enclosed machine soon. The A1 is fine with PLA, PETG and TPU. The following is all related to FDM printers that print from a spool of filament. I have no idea about other process types.
What materials you can print depends on the machine.
A machine with a temp controlled enclosure allows you to print more. Stuff like ASA, ABS, PA(Nylon) and more advanced filaments need (or are drastically inproved by) the stable warmer printing environment. They also need to be printed with a higher nozzle temp.
Sime printers don't work well with TPU and other flexables due to the extruder design, but I think most newer printers do. They need to have the extruder drive in the print head so they are pulling the filament in and have in internal design that correctly constrains the filament between the extruder gears and the heated nozzle input.
"Heat proof" depends on the filament glass transition temperature. PLA softens at a low temperature 60ishC, PETG is a bit higher at 80ish. ABS ASA are higher still. Nothing is heat proof as you are melting it to be able to print it.
Food safe is a bit of a strange one. Most of the filaments themselves would be food safe BUT due to the nature of the way they are printed the surface isn't completely smooth and may have small voids etc which could/would make cleaning difficult and so could harbour bacteria. 3d printed objects themselves would not be considered foodsafe without some form of coating afterwards. Also filament pigments may make stuff non foodsafe.
As for inherent weaknesses. Normally the weakest part of a print is layer to layer adhesion. So prints require orienting correctly to have the best strength characteristics. Different filaments behave differently. TPU for example sticks like s**t to a blanket. Strength is related to the material it's print orientation and the the area that would need to break. There are loads of 3d printed carabiners and hooks out there but I wouldnt use any of them if my life depended (literally) on it. I would give them a go for holding bags etc. Best to test them before relying on them though. Printed things can be supprisingly strong.
I saw a print the other day for those rings used in blokes gymnastics. The guy that uploaded the file said that he had tested them and they worked fine! I can see that the nature of the print would mean that the layer to layer bonding wouldn't be a problem and I suppose there are crash mats under you anyway but still....
As to what I print. It does help if you like making models in CAD, then you can design exactly what you want. I've made custom screw on funnels for refilling things. Custom sized shims to fit bookcases to uneven walls. A stand that stops the families various electric toothbrushes falling over and stops the toothpaste scunge that invariably ends up under them from spreading all over the bathroom windowsill. Simple rings that mean that heinz soup cans stack properly on the cupboard. A thing that goes over the cap an tomato puree tubes so that they will stand up without falling over. A recipie book holder that swings down from under the top cupboards.
There are loads of things that can just be downloaded. Various whistles for the kids (Every time I regret it almost imediatly but somehow don't learn). Masks. Fiddle toys. Articulated toys.
I haven't uploaded all my models but some are on my makerworld account. Username is the same as on here.
Hope that helps a little. It's a big subject.
Cheers
Grebby