RE: Change the names and descriptions of fields
Depending on what exactly you are asking for can already be done by following this tutorial on how to change text and labels in Connections.
RE: Assign which fields are mandatory
This is on the todo list and will be added to the Field Configuration settings when it is added. No ETA on this as I’m working on items for Connections at the moment :)
RE: Eliminate fields which we do not want/use
Checkout the options under the Field Configuration tab on the Connections : Settings admin page.
RE: Add a checkbox field for tags that could become searchable by users.
Tag support has forever been on the todo list. Most often I find that clever usage of categories can work well.
Thanks for the feedback! all of it has been noted.