how do i get these badges to appear on my profile? \

Tenure (the one on the left) is only shown when you have an active Game Pass Core (formerly Gold) or Game Pass Ultimate subscription. If you haven't had a subscription, you wouldn't show the tenure. If you just restarted a subscription, it can take some time to show back up.

Not much is known about the Gold badge. That was given to commemorate the ending of Gold. It's thought that anyone who had Gold at that time would have been given the badge. So if you didn't have Gold at that time it could be why you don't have it. There are also still people waiting to see if the badge will be added to their account.

It should automatically fall off on its own, but you can email xboxambs @ microsoft.com (remove the spaces) to contact Ambassador staff to see if they can remove it.

how do I get my forum badge ?

On my sisters profile her badge appears though why would mine just stop though

Are you an Xbox Ambassador?

There is a tab for 'Profile' then down below click 'Badges & Pins' and you can toggle on or off for your badges to appear on Xbox Live profile.