sweetmikey,
First things first, please try to not write in shortcuts and abbrivations. It is very annoying to read it and to decypher what you're trying to say. This isn't a cell phone where characters are limited. So try to use proper English words. It is benefitial for everybody and speeds things up (as we don't need to take some time to decrypt everything)...
Anyways, as you could guess, Messenger has sometimes syncronization problems. The results are that you sometimes have weird things happening like statusses which don't update of added people etc. Most of these problems can not be fixed from your side. You just have to be patient as the fixes are protocol related and thus should be done by Microsoft themselfs.
Then there are also the normal scenarios which might confuse some people. Eg: if you are talking to someone which isn't on your contactlist (I'll get to that later) it is possible that their status has just changed from online to appear offline. When people are appear offline they still could talk to you and you can still talke to them as long as your conversation window is open. This is called offline talking (not to be confused with offline messages).
As for your first post in this thread. When you click on 'add this person to your contact list' it is again possible that their is a syncronization problem (which you can't do anything about it). I wouldn't worry about it too much. Of course it is annoying though...
Anyways, the most important thing I would do is enabling the option
"Only people on my allow list can see my status and send me messages". Because as it is now, I think you do not have that option enabled.
Enabling that option is a lot safer for you and will protect your privacy more. Random people wont be able to start talking to you. People could still add you to their contact list and you will get a warning when they do though. It will also make things a bit more logic as in who has added you or who can delete who, etc.
Tools > Options > Privacy > "Only people on my allow list can see my status and send me messages"
And last but certainly not the least: edit that image and blank out the email addresses. It is a huge privacy invasion to show email addresses from people like that. You probably don't like it that you get a lot of spam in your mailbox, other people don't like that either. So please do not post or give email addresses of people in public without there consent, not in text, not in images...
As such, here is the screenshot without the email: