I figure their internal Light helps a bit with fortitude and resistance, but overall they're still just regular humans/exo/awoken until their ghosts top 'em up. Several lore pieces mention grave injury before being specifically healed by ghosts.

Now, if their ghosts wipes their butt or not:

• Zavala's: yes
  
• Ikora's: it better
  
• Cayde's: it once lost a bet, so yes
  
• Drifter's: hell no
  
• Crow's: he doesn't even know how to on his own yet

Just in one of those moments, I was curious how The Light affects guardians in basic medical and biological ways. For instance:

• Can guardians get drunk?

I think it's mentioned several times in the lore, but yes. Hawkmoon's text describes the Crow getting so drunk he can hardly stand.

• If they lift too much, can they slip a disc or pop a hernia? And if so, will the light just heal it right back?

Yeah, they can suffer normal injuries when exceeding their limits. Crow had his legs broken when chasing the Celebrant, but was still communicating with us. No telling how long it takes Ghosts to heal them, but I imagine it's just a concentrated blast of Light away.

• Do you think when they stub their toe in the night it hurts like hell?

They scream in pain from landing on rocks funny, so probably!

• What about colds, flu and such. Or you know...other "social" ailments?

I think that we are immune to disease ("Good thing we can't get Tetanus!" - Ghost).

• Is there a dry cleaner in the tower? I have to imagine most guardians are covered in all kinds of nasty stuff.

Given that Ghost materialized a full set of armor from nearby junk, I imagine they can transmat grime and dirt off us fairly easily.

• Do guardians sleep?

Funny you should ask! All guardians sleep, but Exos share a recurring dream of the Deep Stone Crypt. It's one of the neater pieces of lore.

• When they are out and about and nature calls, do they just take care of business and then are like "hey ghost, a little help?" and then just, voila, all clean? (I actually have a lot of questions about this topic, but, one thing at a time.)

Slow down there Rowling. But also, remember that Crow has a makeshift toilet in his Nest (complete with oddly-intact toilet paper rolls), and he likely never expects company.
Elsie also has a well-equipped toilet in her hut, though that raises even more questions...

• How come ghosts will follow us everywhere except off cliffs? Guardians will be like "I wanna go down here!" and ghosts are like "Nope, I stop at the edge."

The last punchline of my fan fiction story!
I wonder if they're just making a copy of our Guardian. as we can sometimes revive in time to see our mangled corpse. Again, even more questions... That said, I think the official lore has Ghosts manually reviving the corpse, except in the event of disintegration, during which they can apparently make a clone of us (which is why Felwinter killed a Ghost after vaporizing the Warlord Guardian.Mixed up that story with Callum and Shin).