I applied for an installment plan to pay off my federal taxes. How long does it typically take the IRS to send information whether I was accepted and when payments begin?

Payment plans take weeks to approve so the payment will not happen until then ... they will send you a letter when they decide but for now you can expect the payment to happen anytime now ...  OR  you can make payments directly on the IRS web site now ...https://www.irs.gov/payments

I got my acceptance letter on 3/14/18 and I still haven't had anything withdrawn! It has been 12 weeks since the letter... should I be concerned?

Yes you should ...review the debit info for correctness.