How do I determine if my BASD, PEBD & BESD are correct? Does my active duty time not count?

Your BASD is irrelevant since you're in the Reserve Component. If you rejoin an active component your BASD will be recalculated. It's only used to calculate your time towards an active duty retirement, if you're not on active duty it's not applicable to to you.

Your PEBD is incorrect and should be around 2013. What your ERB says isn't as important as what your LES says. If DFAS is tracking the correct date then you're getting paid correctly. But your PEBD does still need to be updated because that may affect your TIS for promotion

I have had mine adjusted due to transitioning from active duty to the guard and then back to active duty. It is really confusing how they do it. but as did it before you pay entry basic date will stay the same unless there is a period that didn't qualify. I had a year and a half break of service where I wasn't in the IRR. All of my other time from being a reservist and an active duty accounts still. So my pay visit entry date was adjusted to reflect as if I only had one period of service minus all the breaks. Basically if you did four years and then went to irr only to join the national Guard again for four years before getting out that would count as one period. If you came back to yours later into the military they couldn't count those two years as credible service for pay so they would move your years of service two years to mitigate the gap.

You need to go to your state hq’s and ask to see the retirement NCO. They will take all your documentation and calculate your correct PEBD & BASD.

Do a review of your RPAM first with your admin NCO. Make sure your Iperms have all orders, DD4 and reenistment documents. Match them against your RPAM statement This. This would help to make sure all service time is correct.

Submit a 1506, have the adjutant or retention verify it and let finance encode it in the system

Your active duty time counts. You should be able to get the date added with a copy of your DD-214, unless I'm mistaken. It's been a while since I retired, but your time counts.

There is a calculation form they use to determine your dates. I still have mine, lol. I was active and then got out for 12 years then joined the NG for three years, one year deployed, and did an RC/AC transfer back to active duty for 14 years until medical retirement. So all three were different for me, BASD and PEBD were the most important to have right. Get with your retention NCO and have documentation for all your dates. It's an easy fix and important to have correct.
I'm just going by my personal experience.