Following is free and costs you nothing but attention. Membership is an annual subscription, and everything the network actually offers sits behind it.
The difference in one line: a follower reads, a member takes part.

Three routes, and only one of them involves paying.
Check Memberships under your profile picture before you buy anything. A registration or a grant may have given you the membership already.

Membership includes a personal subscription to everything the network publishes — its journals, its books, its conference proceedings.
You see it at the point it matters. Open an article, and a member is offered a download where a visitor is offered a price.

Under a community’s More tab, a control switches between Member, Follower and Admins, with a count above the list. Every row offers Invite to peers.
It is the best directory of a field you will find, and the fastest way to build a set of peers who actually work on what you work on.

That button belongs to members. If you are following the network rather than a member of it, the feed is read-only.
Your profile picture → Memberships lists every membership you hold, with its source. Anything not listed there, you follow.
If the registration type was marked Grants Membership, yes — and it will be in your Memberships list. Not every type carries it.
Per network. Each one is its own membership. What they share is the account, the profile and the wallet.
Yes, and it is a reasonable way to decide. You will see what the network publishes and how active it is before paying anything.
You keep the account, the profile and everything you have published. What you lose is the access, the discount and the ability to post to that network.