The Arbitrator (and not a court) likely has authority to decide whether the parties must arbitrate and whether their contract (as a whole) is valid (Buckeye Check Cashing; Rent-A-Center). (Yes, you can be forced to arbitrate based on a clause within an otherwise unenforceable contract.)
Piecemeal litigation is “A-Okay”; efficiency is not the goal of the arbitration acts (KMPG v. Cocchi).
The bases for “appeal” of an arbitration are incredibly narrow (9 U.S.C. 10; Sutter), so the award is generally the final word.
Parties must preserve any bases for vacatur by raising them with arbitrator (if those bases were known or could have been known) (Dealer Computer Services). (In other words, if you may want to appeal your arbitration award based on arbitrator bias, you first have to tell the arbitrator you believe she is biased…)
There is still significant judicial hostility to arbitration. Even when you are arguing for arbitration, and the case law is on your side, a court may still find a way to retain jurisdiction or vacate the award. (Examples here, here, and here, and almost every week on this site.)