Is it actually passing an entire transaction hash to the subroutine?

Kind of. It's passing a reference to an entire transaction hash to the subroutine. When we refer to the $$hr{type} value, it first looks up the address of the hash with the innermost $hr part. Then it looks up the type member of the hash that $hr references.

Would I do the DB insert in the complete_xxx($hr) subroutines?

I did in my project, but you certainly don't have to. You could build a reformatted file that you can load into your database with a bulk-loading tool, like BCP (in MS SQL).

Should I store all the complete transactions and then insert them all, or should I constantly be having it insert transactions?

You can do it either way. I tend to insert them as I go because some of the files I work with are large, and I don't have enough RAM to hold it all in memory. But if all your data will fit, you can do it that way if it's easier.