Most pilots have a speeding ticket or two in the past. I would estimate that 2 in three years is about the max before they start having doubts. Also it helps if you were very young, and those tickets were in the past. Since you will not be apply to an airline anytime soon, you need to keep a clean record going forward. It's easy, I haven't had a ticket in years although I got at least one a year when I was young and driving navy-funded high-performance sports cars...drive speed limit+5, come to a full stop, don't do crazy lane changes. If you're doing a road trip, your spouse/buddy will complain that you're going too slow...so let them drive. It's much better now that the speed limit is 70+ on the open road.

The revocation is a little more of an issue. That will probably show up on your NDR and you will have to explain it to the FAA when you get a medical. The FAAs only interested in whether it was revoked for dui or refusing a breathalyzer, they will not care about a revocation for admin purposes.

Airlines might consider failure to pay speeding tickets a sign of irresponsibility...hopefully you have a good explanation: moved so the notice got lost in the mail, lost job so couldn't afford it, trying to to appeal it in the court. I would not admit that you just decided not to pay it.

The airlines, FAA, and the TSA all have separate background checks.

The airlines vary from the standard "call a few references" up to a serious check conducted by an outside BI firm. They will also review certain flight training records from the FAA and past employers (PRIA).

The FAA will look at national databases EVERY time you renew your medical. DUI or real crimes will cause problems. Too many speeding tickets (a lot) might cause problems too. The FAA will look at this from the perspective of mental health/stability.

The TSA requires a background check of all airport employees, this covers a very specific list of serious crimes going back ten years. This is pass or fail, no grey area. You can google the list.