Yes, cascade counts as casting, The rules for cascade explicitly state, you may cast that card without paying its mana cost. This means that cascade can be blanked by cards like Rule of Law or taxed by effects like Rhystic Study
Tapping a creature thats equipped doesnt tap the equipment attached to it, and tapping an equipment doesnt tap the equipped creature
For example, if you have a bunch of designs that require 5 x copies of each to be included, move them into a folder called "5" or "5 copies"
If you want to build a variation on Party Time with Tazri, I'd have you drop out the underperforming, overcosted cards that play better in sealed and draft and add in more removal and a few boardwipes
As for the favorite noncommander card, its this: Im on record as loving Sunbirds Invocation more than most of my family
Collectors shelves are lined with multicolored Trainer Boxes, plushes, and figures depicting their favorite Pokmon