Have any Aes Sedai ever been refused admittance to any Ajah?
No. (see below)
Can an Accepted be raised to Aes Sedai and not choose an Ajah? What happens if they are raised ask for acceptance and are refused?
This never happens. They are chosen in advance and vetted.
If you are viewing this on github.io, you can see that this site is open source. Please do not try to improve this page. It is auto-generated by a python script. If you have suggestions for improvements, please start a discussion on the github repo or the Discord.