I have a problem with my account.

If your account is over the age of 18 you must promote it

By removing it from under the control of the parental account

And no changing the ms account nor the age of the acount after the fact won't promote your acciount

It goes by the original dob on your account not future chcanges

Removing it before the age of maturity will only force you back into it by requesting a parental account

Sorry but you must be over the age of a minor as defined by the country you are in. Also if you are an adult and you age is correct on your account the other reason I've found is that your account is managed by a family parent account. If this is the case
then your will always be considered a child account as this is what they are considered no mater your age.

Can you please check you account to make sure there are no overdue payments or subscriptions.

https://account.microsoft.com/services?lang=en-gb

If you do you will need to clear them before you can continue using your account.

try removing the account from the console, doing a hard restart, hold the power button for 10 seconds while the system is on, and then re-adding the account

The Xbox Insider hub has no effect on the 360. As for your messages on the 360, it does not save your sent messages. You should be able to see and read them either from the Xbox One console or xbox.com.