1. Is there a way to gauge how many brushes or materials one has on a wand, or no?

2. How many times do I have to use Absorb to attain the amount of brushes required to use Bridge, or Toss, or Volley, etc.

1. It tells you in your wand's lore: https://imgur.com/a/651eH

2. They are unrelated, you should be able to use those spells right away. They don't work with the erase brush, but should work with basically any other brush. You get a handful (dirt, etc) when ranking up to engineer so the spells should be available immediately.

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