Domains like .tk will be pushed down in Google results, you will have issues when you will try to send mails from such domain, etc. If something is free and attractive it's usually abused.
If you don't care about such things and you can easily move to another domain without any issues (people still accessing old domain, maybe finding a scammy website after domain is being taken from you, your mails no longer being delivered to you) then go for it.
No, you can use a domain address you have gotten elsewhere and have it resolve to your GitHub pages. I’ve been doing this for awhile and have never paid a penny.
If you don't care about such things and you can easily move to another domain without any issues (people still accessing old domain, maybe finding a scammy website after domain is being taken from you, your mails no longer being delivered to you) then go for it.