1) You can grant me that community builder and CB Connect work this way?
CB Connect has a Facebook Social Plugin field to render Comments. Facebook exclusively renders this display (CB Connect has no control over it) and it always includes the avatar. You don't need CB Connect for this though if you just want the Comments Social Plugin. See the below on how to add it to your site otherwise CB Connect can do it using a Facebook Social Plugin field.
developers.facebook.com/docs/plugins/
2) Since I'm using hotspot on my site, and as hotspot supports only ccomment for the comments, I'll use ccomment at least in the map. On the reference site tell me that ccomment displays the avatars that are saved in community builder. So I want to know if by registering through facebook, community builder is able to store the FB profile photos.
Commenting with Facebook always shows the Facebook avatar. It will not show the CB site avatar. There is no changing this.
3) Which subscription should I do? Advanced or Professional? I just need the features that I have described.
CB Connect is provided with the Advanced subscription and up. So whichever of those you prefer.
I urge you to try the social plugins without CB Connect first to ensure they'll meet your needs as they'll function exactly the same in CB Connect.
krileon
