Riffing on this thread.
For me:
Defecation: downloading Republican talking points.
Piss and shit. I’m a man of simplicity.
My Daddy said “Gonna see a man about a horse” for peeing.
I shouldn’t say this, but it took a Doper to explain it to me. Sometimes I’m dense.
For respirations: “I need to breath now”.
When I need to ingest nutrition at mid day: “It’s time for lunch”.
When it’s hot out and the humidity is high: “stand back, I’m gonna break a sweat!”
;-D
Very bad cough: I’m harking up a lung.
Huge belch: Must be a barge coming through. (Thanks, Mr. Watterson!)
When I’m shooting my load I scream “Release the hounds!” 
Defecation: Dropping off the kids.
Urination: Gotta go swing a big deal.
Farting: stepped on a duck
Hit the whizzer.
I knew a guy from Texas who said he was going to see a man about a dog. For the longest time I thought he went to see a man about a dog.
If my Daddy burped he said “Sorry I thought I was in the Officers Club”
He was an old Marine.
Pinching a loaf for pooping disgusts me.
I drive people around in a bus for a living, so I use ‘Pit Stop’ as a reminder before we are doing a long-ish stint.
I call it “dropping the kids off at the pool.” For defecation, I’ll also say, “I’m taking the Browns to the Super Bowl.”
I used to report the dogs activities as “evacuated her bowels” and “voided her bladder” until my tween daughter asked me to say “pooped” and “peed” instead because my terms were gross. After she googled them.
When I was a kid, my mother used to refer to pooping as “doing a job.”
And then there was the paperwork after the job. 
Drain the lizard and take a dump.
My wife always says it took her 5 years to convince me to stop saying piss and crap.
It is true. It did take a few years for me to change my slang. I can say time for a dump without worrying about being overheard in public. My beloved knows I’ll be indisposed for at least 10 to 15 minutes.
I grew up in Texas, and one of my friends there was out with a bunch of people and one of them said, “I have to go pick up my sweetie at the airport.” She thought that was the cutest euphemism she’d heard for it, except it turned out he was actually going to pick up his sweetie at the airport.
This is an event that requires an announcement? Do you folks really specify what your needs are prior to entering the bathroom?
mmm
For #2, I often think of “blast a dookie” (snowboard language, according to The Simpsons) and “blow some snags/snaggers” (learned from an Australian classmate).