Rek'Sai Breacher gives your units Accelerate. Do they still pay to Accelerate? Also, what rune type do they pay? Since Rek'Sai is 1 Energy 1 Fury?

Yes, you still have to pay to use Accelerate, even when granted by Rek'Sai, Breacher.

Accelerate is never free; it is an optional additional cost that gives you the choice to have a unit enter the battlefield ready instead of exhausted.

Payment Details

According to Rule 805.1.a and Rule 805.1.a.2, here is how the cost works:

1. The Cost: The cost is [1] Energy and 1 Power.
2. Rune/Power Type: Since most tokens and many units affected by this ability either have no domain or multiple domains, the Power portion can be paid with [A] (a Power of any domain).
   • Even though Rek'Sai, Breacher belongs to the Fury domain, you do not have to pay a Fury Power to use the Accelerate granted by her ability. You can use any domain's Power.
3. Payment Timing: You must pay this cost during the "Pay Costs" step (Rule 357) of playing the card. You cannot choose to pay it later once the unit is already on the board.

If you choose not to pay this additional cost, the unit will simply enter the battlefield in its default state, which is exhausted.