Okay I will put aside my shame and vow to answer all of these, without looking at the questions up front. (Unless the answer would reveal anything identifying about me)
1. Have you ever peed your pants in school?
No.
2. Have you ever ACCIDENTALLY peed yourself as an adult?
Yes, I remember one time that I started to pee before I took it out, thus peeing all over my pants. Fortunately I was at home but I did have my mom visiting. She just laughed about it and shrugged.
3. Have you ever been caught naked by your parent(s)/child(ren)?
Not that I recall.
4. Have you ever caught your parent(s) naked?
Not caught, no.
5. Have you ever had your sexuality or kink outed to a family member?
No. Well my sister did once find porn pics on my computer and told my mom about it, does that count.
6. Have you ever had sex with someone, only to learn you were related?
No.
7. Have you ever had sex with someone, only to learn they were married?
No.
8. Have you ever been caught having sex or masturbating by your parent(s)/child(ren)?
No.
9. Have you ever caught your parent(s)/child(ren) having sex?
No. Are my answers starting to bore you?
10. Have you ever been caught farting in a public (polite) area?
Not that I recall.
11. Have you ever had an upset stomach on a date that ended in diarrhea, gas, or vomiting?
Not that I recall.
12. Have you ever been called out for having smelly gas?
Not that I recall.
13. Have you ever had a credit card declined and/or had to endure the "Walk of Shame" while returning your items because you can't buy them?
Something like that. I had my debit card not working or I forgot to bring my money. Nothing embarrassing about this I think.
14. Have you ever fallen down a flight of stairs in the company of others?
No.
15. Have you ever sent an AWFUL drunk text, or drunk-dialed someone?
No. Really, it is the truth. I am so boring to the outside world.
16. Have you ever been caught talking behind someone's back, by the person you're talking about?
Most likely, but I can't recall.
16. Have you ever accidentally sent a scathing text message about someone to the person it's about?
Yes I have. It was indeed embarrassing but I really can't recall to who and what it was about. Sorry.
17. Have you ever accidentally sent a "sext message" to an unintended contact?
No, but since I am a sub to Miss Butterfly, I did actually almost call a female colleague 'Miss' on chat. I have to really take heed of that.
18. Have you ever clogged a toilet after pooping?
Yes I have. I think it was in an airport toilet somewhere.
19. If you experience periods, have you ever bled through your clothes?
n/a
20. If you died right now, what would be the most embarrassing thing someone would find in your house?
My porn pics collection, the extreme ones in particular. IF they can actually find them. They are hidden under a second windows account so they should have to crack the password or access them some other way. They are more likely to find my toy collection which is now ever growing. That would be embarrassing but since I'm dead, I would not care about that.
21. Are there any unwanted nude photos of you floating around the internet?
No. I sometimes wanted to share nude pictures. I still do. I am not embarrassed about sharing them with select people. But the problem is indeed that everything that comes on the internet you can never get back. So I probably never will.
22. Have you ever fallen prey to an internet scam?
Not that I recall.
23. Have you ever made an idiot of yourself in front of a crush?
No.
24. Have you ever argued with an authority figure only to find out you were VERY wrong?
Not that I recall.
25. Have you ever been in jail?
I have visited Alcatraz, does that count? 
26. Have you ever come to the realization that you've been walking around with your pants zipper down, or with a hole in your pants?
Yeah, zipper down. But I didn't think that's such a big deal. I still wear underwear and you can still not actually peek inside so easily with the zipper down.
27. Have you ever accidentally walked in on someone in the bathroom?
No, but I have it happen to me while I was pooping. That was pretty embarrassing.
28. Have you ever accidentally told someone you loved them?
No.
29. Have you ever accidentally called someone mom or dad?
No, how can that happen?
30. Have you ever had a crush on a teacher?
Oh yes. My English teacher. She was deemed a bitch by many and I get what they meant. She ruled the class with an iron fist. But she was still a good person, I respected her, she looked gorgeous and I loved her.
31. Have you ever had a crush on/fantasized about a cartoon character?
No. But I do think Yennefer and Triss Merigold of The Wither computer game series are gorgeous. But I don't think they count as cartoon characters since they are very realistic.
32. Have you ever eaten at a restaurant only to find out the bill was WAY more than you could pay?
No.
33. Have you ever spilled drink or food at a restaurant?
Yeah, quite a few times. Annoying indeed but not the worst of embarrassment.
34. Have you ever been denied a kiss on a first date?
I never tried that on a first date so no.
35. Have you ever been caught trying to cheat, scam, or steal?
Nope.
36. Have you ever set off a store alarm while trying to exit?
Yeah, because they forgot to take off that alarm triggering thingy. Their mistake, not mine.
37. Do you get zits in noticeable places?
On my nose sometimes. That is never annoying and unappealing since my nose is already quite big in the first place. I really don't want to have any added attention to it.
38. Have you ever had your pubic hair get snagged by your clothes?
By my zipper you mean? Yeah. But that can't happen no more since Miss has decided I should shave it all off.
39. Have you ever gotten a REALLY bad itch on your genitals while in public, so you couldn't scratch it?
Yeah. And in Miss' butt crack too. It's very very annoying.
40. Have you ever finished on the toilet only to find out that there's no more toilet paper, then have to do the "Walk of Shame" to the closet (or, if in a public bathroom, to the next stall) to find some?
Yes. That happens sometimes at home which is particularly annoying when I have diarrhea. But since I live alone it's not embarrassing. In public I think it happened once and since then I always check up front if there is any.
Thank you for the questions. I had fun answering them but as you see, I haven't had many embarrassing moments.