Can this bike be saved from the rust? So, I'm buying a bike to use during a summer before I go back home. I found this bike that I'm interested in buying however it's extremely rusty. I'd like opinions on whether this is a DIY clean up, or if I'll have to spend a lot at a bike shop. I have 0 knowledge of bike repair/maintenance, so if it would involve anything more complicated than rubbing it down with some product/aluminum foil, I need to know. Thanks]1
Anything is fixable given time and effort and money.

You need to decide first whether the bike fits you, and will do the job.

Then decide if its safe - do the brakes work right?  Does it stop and go okay?    Are there and thick patches of rust?   Poking at any suspicious rust with a pen will show how deep it is.

Consumables need checking too - depending on its history and recent storage, you may be up for 4 new brake pads/blocks, 2 new tubes and 2 new tyres immediately.  Look for cracking in the tyres, whether it holds air at full pressure overnight, and how hardened the brake pads are.



Fenders/frames
If you want to fix the rust, you could simply paint over it, but that fix will last months at best.

Remove the rust physically by sanding or foil and then painting, and it will come back after a year or more.

The best fix is to chemically treat the rust with a rust killer like Phosphoric Acid, which converts the brown/red rust into a stable white or black iron oxide.  Then you sand it and paint over.  This should last the longest.

Rims
Much harder to deal with - because anything put on the braking surface will wear off quickly under braking.  Best technique here is to scratch the rust off using a brass brush, and then apply the phosphoric acid to treat the bits you missed.  Ideally do this with the tube and tyre off.  And mind your skin - this stuff is nasty.



Finally, based purely on the picture above, it looks like cosmetic surface rust.  So if this is the case, you're probably able to simply ride it as-is.  Bonus, makes the bike less attractive to a thief.