"much better than Access 97,"
Anything is better than access 97 🙂
InnoDB is a table handler for mysql, it integrates into mysql (check the manual)
PostgreSQL is a completely different product that would replace mysql completely.
About indexes; read the mysql manual, it has plenty info to feed on.
Indexes have nothing to do with relations at all.
You can build a tree with leaves using MySQL with InnoDB, but you can't use cascading deletes etc to ensure that you always remove and entire tree/branche, and not just a few parent nodes (leaving orhan nodes and leaves)
You have to write a script with multiple queries to safely remove a tree.
A forum, a FAQ, email notification, what else do you need?