Amazon Fire TV Stick explanation?

I want to buy an Amazon Fire TV Stick to watch Netflix, etc. But I have an old TV (no SmartTV). Is that still possible? So I just have to put it in and you're done or how? And do you need Amazon Prime?

You need a HDMI port and a normal Amazon account, Prime is not required.

The FireTV-Stick replaces the "Smart-TV". You only need an Amazon account and if you want to watch Netflix, of course, a Netflix account

You do not need a Smart TV for this (otherwise you probably do not need a Fire TV Stick). The stick only needs an HDMI input on the TV.
No, you do not need Prime for that.