Welcome to AAPK
and congratulations on having a family heirloom knife. Those are really special!
You've asked enough good questions to require an entire essay to answer them all so I'll try to be brief. Your knife doesn't appear from the pictures to be badly rusted. The veteran collectors here on AAPK have stuff we've purchased especially for knife cleaning. I'm gonna assume you don't have any of that, so my recommendations will use stuff you likely have on hand.
First I'd apply a thin coat of light oil (like 3-in-1 for example) to the blades. Let it soak in for a few minutes or so, then rub it off with a soft cloth. Much of the rust will disappear. If any remains use a sharpened number 2 lead pencil, rub on the rust with the "lead". This is a very mild, fine textured abrasive. Wipe it off, repeat as needed.
If that still doesn't remove it, turn the pencil around and use the eraser end. This is a more aggressive abrasive but still fairly mild. Rub the offending spots with the eraser, gently at first. Don't rub any harder than you have to! Wipe the blade after each attempt to see if you can stop. Don't do any more than you have to. Don't rub on any areas that are not tarnished.
If you have any metal polish, such as Mothers Mag, Semi-chrome, Flitz, or similar, use as directed. I doubt you'll need anything more aggressive on the pictured knife. If there is any dirt, lint, etc in the blade wells it can be removed with a cotton swab, or a soft cloth or tissue on the end of a match stick or broken toothpick. Some rubbing alcohol or light oil on the swab may help and won't hurt anything in the blade wells, just be sure to keep it off the handles, which, given its age, I suspect may be celluloid. (See here for some techniques for confirming celluloid viewtopic.php?f=4&t=50712&p=542630&hilit=Celluloid#p542630
. Havent tried these personally - you're on your own there!):lol:
Go slow, be patient. A little slip or going too far too fast without checking your progress can inflict damage that can't be reversed. When you've finished wipe the blades with a light coat of oil, put a drop (one drop) into each blade hinge and work the blade open and closed a few times. Wipe off any excess. You're done! I doubt your knife will require anything more extensive than what I've outlined but just in case it's more severe, see this AAPK thread for recommendations. viewtopic.php?f=38&t=47909
If you decide to carry it, given that it's an heirloom I'd get a knife pouch to place the knife in while its in your pocket. Similar to these https://www.etsy.com/shop/CIRKLEBLEATHER/items
, or these https://www.knifecenter.com/item/SK803/ ... ix-pouches
. Or you can make your own out of felt, if you can sew a little (or know somone who can do it for you). This will protect it from banging around and being scratched by other stuff in your pocket, like keys and coins.