Okay, this time, I want another follower besides Faendal who can teach me archery. I was wondering if it is possible to have Aela as a follower after the werewolf mission.
Werewolf "mission" (correctly called a quest) is a vague term to use, but it depends which quest in the quest line you are referring to. If you are referring to the start of the companions quest line then no. Aela only becomes a follower after completion of the entire companions quest line.
Yes, you can. Additionally you can also marry her, but that's not what you're asking.
I'm not sure what the requirements are to get her as a follower - whether you can get her straight after the first werewolf mission, or if you have to finish the entire Companions questline.
Yes, you can absolutely have Aela as a follower.
But word of advice, she isn't very good at fighting. She will not die but her life drains away very quickly in a combat thus all enemies will be focussed on you.