Agreed! About 20% of the reads cannot be joined, but this is pretty good given the quality.
ITS classification is harder than 16S classification for a number of reasons. For a first run with a custom database (that you just made!), I think getting to order is pretty good!
Yes. It's all about classify-consensus-vsearch.
Aftering finding hits to the database with vsearch, the taxonomy of these hits are compaired. For each level where >50% of the hits agree a classification is given, until you reach a level where there is not longer a consensus.
For your data, the level in which hits no longer agree is mostly Order. 
Your progress here is awesome. If I were you, I would keep these results and continue with the paper. If reviewer 3 thinks there is a better way to classify ITS-2, they will certainly tell you.
EDIT: If you do want to improve the database, try using RESCRIPt's 'extract-seq-segments', or adding a few "out-group" taxa to your database in case you amplified non-Magnoliopsida taxa.