I don't think such a thing exists. What are you trying to do/what are you unsure about?
I've seen other users delete their own posts so it's definitely something that's enabled. I would expect it to be done via clicking the Edit button on a post. Maybe you can only delete posts in a thread that's yours. Try one in this thread. It's hard to tell for me because I'm not sure which options everyone has and which I have because I'm a moderator. I need to make a test account again. Won't have a chance to do that until tomorrow though.
The profile visitor feature shows you who has looked at that profile. So if I visit your profile (https://guildwarslegacy.com/index.php?user/2078-lady-lyn/) while logged in it'll list me and the timestamp in the visitors section. It's not something you do manually, nor is it something you necessarily need to do anything with. It's just for personal interest, really.
I'm not sure why it's not tracking your activity. Maybe you weren't logged in at the time, or your account is somehow set to not appear on such trackers (invisible status?). Maybe you just need to refresh the page, though that's not the case with me. Try visiting my profile and I'll check if it comes up for me.
As for deleting single posts, then yes that's Edit -> Move to Trash -> Dialoge asking for reason -> OK
As for an an activity log - I guess the closest is -> Click profile -> Post count next to your avatar
To delete posts there would be a bit cumbersome, you would have to open each thread individually from there. If this is a wanted feature, maybe you could encourage Iaerah to add an "archive" button. But that might be tricky as each thread might have their own priviledges.
Thank you both very much for your answers,
looking at my second post though, I could have been clearer.
I was referring more to the profile activity log, and not the actual activity itself.
More or less removing the table of contents from a book, without touching the actual contents.
On PSC we could clean up a log without it affecting the actual posts.
I wished we'd had the same option for old notifications as well.
It's kind of like storing old "to do" or shopping & other sorts of lists.
Once "to done" and bought they're more or less useless.
What ever isn't done or bought heads a new list......
Also, I looked about and I don't believe I'm set to invisible...
I'm wondering if you just don't see your own footprint because you're standing in it,
so to speak...that could be the answer.
When you visit my profile, do you see yourself as a visitor?
While I'm here 
What exactly is the difference between profile hits, and profile visitors?
Forgive my ignorance of the subject,
I'm really not a big forum person, so I don't know my way around different formats.
I've only ever been in 3 or 4, and all in the last 10 years.
I joined the original Presearing Community in 2008, but never did anything with my profile.
I think I was put off by the use of the word noob, so I was hesitant to ask for help.
When that one was dissolved, it was PSC at the end of 2015.
I had to learn fast starting in May 2016, when I was added to the admin team.
(I needed to be able to answer other members' questions.)
I learned to do the most on that one, picking up minor code and other things.
My kids kept trying to get me to join this forum, because it's a "Whole Game" forum,
but I was too busy, wrapped up in creating guides for the other.
I finally listened to them and joined.
It is very similar to the original Presearing Forum, which I never learned to navigate well.
I finally joined reddit too yesterday just to keep an eye on the game updates, mind boggling!
No worries there for me though, I'm just a passive GW update reader 
profile hits is the total of all users that have looked at your page (grand total), profile visitors is usually the last few users that have visited--however, one user can visit more than once so they will only show up as a visitor but can count as more than one profile hit.
I think you dont see yourself as a visitor to your own profile because--its YOUR profile, but it might count towards the total hits. ( I could be wrong, this software is new to me as well).
