The glands are part of the immune system/lymphatic system. Yes, it's perfectly normal for them to swell during an illness - that's the body's immune system doing its job. So it's a good thing! (Don't start thinking "abnormal lump" - it's not!)
It's not always from a cold - it can be from other things (viral or bacterial). Almost none of them are a matter of concern - and your child has all the other symptoms of a respiratory tract infection, so there is no need to panic about other things. A week or 10 days is normal duration for a cold, and changes in BMs are common especially when a lot of mucus is being swallowed. He's got nasal discharge, but I'm sure a lot of it is going down his throat through post-nasal drip. That can also upset the stomach and make someone a lot less hungry. Plus he's probably not running around as much because he just doesn't feel well, so he's not burning up the calories. He needs fluids far more than he needs food.
What you're describing is irritating and frustrating and it sounds perfectly normal. Increase fluids as much as you can (popsicles, jello, water), go easy on the dairy if he's got a lot of digestive distress, and rest rest rest. Everyone needs to wash hands - not with antibacterial soaps, but with regular soap that makes a lather/bubbles, and do it long enough. Most kids - and a lot of adults - just squirt some soap on their hands and immediately rinse it off. You've got to lather up for a good 30 seconds (have them sing "Happy Birthday" or the ABC song twice though) and THEN rinse. (Think of doctors scrubbing up for a long time - and they're wearing gloves afterwards!) Don't share towels. Put used tissues in the trash and rinse hands afterwards, and don't let kids touch their eyes after touching their noses - if you can police that! I know it's hard!