Expanding on what Drrek said should answer all of these questions:
Once abilities begin activating, NOTHING can be played until they, and any abilities that activate due to those abilities, finish.
For example, if I use something to band in a bunch of heroes as was mentioned in the first post, that band is not completed until ALL characters have entered battle, ALL of their abilities have activated, and anything else done because of those abilities finish. If I use Deborah's Directive to band a bunch of guys in, and one has a weapon and another has a band, both the weapon and the band must complete before Directive is considered 'completed', and any abilities on the new character banded in must complete before that band is 'completed', and so on until everything stops (and any triggers on cards already in play are resolved).
To answer your other question, once a character enters battle all abilities on their card, their weapons, gained abilities, and any other cards played/added because of them (bands, etc.) must complete before they are considered to have presented for a rescue attempt, battle challenge, or block.