Can I use Rell to equip a long sword for free when she attacks?

Yes. Rell's "When I attack" ability lets you play Long Sword ignoring its cost (both Energy and Power set to 0), and then attaches it to her — no extra payments needed.

Here's how it breaks down:

1. Cost check: Long Sword costs 2 Energy, which is ≤ the [2] limit on Rell's ability. Eligible.
2. "Ignoring its cost" (Rule 353.1.a): Both Long Sword's base Energy cost (2) and base Power cost (1) are set to 0 — you pay nothing to play it.
3. Attachment: Rell's ability then says "Attach it to me" as part of the same effect. You do not pay the [C] Equip cost — that's only relevant if you later want to move Long Sword to another unit after it detaches.
4. Quick-Draw: Long Sword's Quick-Draw trigger ("When you play this, attach it to a unit you control") will also fire, but it's redundant — Rell's ability already handles the attachment to her.

You pay 0 Energy, 0 Power, and 0 Equip cost for the whole sequence.