Need a new sliding door latch

Hello, Don. The internal piece you refer to is called the mortise lock. Yours in particular looks like our 82-218. I'm pretty confident this will work for you.

I have some bad news about the rollers, though. The only way we can ID them is to see them out ahead of time. I know that's more of a project than you wanted to deal with, but it's the only way. That's just how patio glass doors are designed. If we can't see the roller, we can't find a match.

Specifically, we need to see the top, side, and rear. Dimensions would also be a big help.

Finally, concerning your track, you only need to replace that if it's in bad condition.

About removing the stationary door first: in some cases, you need to remove the doors from the outside of the house. In other cases you can lift the door up and out from inside the house. It really just depends on the door. The type we show in our video is just the most common. 

Those button covers you show in your photos I believe are just guides to help center the door. I don't see evidence of any security mechanism.