dunno which version of vanilla you played, maybe you’re one of those players who regards BC as Vanilla ?
Both of these things are exactly as they were in Vanilla. You also have raid frames incorporated into Classic, that wasn’t part of vanilla originally ( at least not with the level of functionality it has in classic ), which gives you the ability to view pets etc easily, you just need to configure it.
The best way to deal with the mounted issue, is make a macro or get a mod.
No, they weren’t. I started in patch 1.4 and it was NOT this way. I pretty much lived in BGs at 60 and I could easily mount run into an ongoing skirmish and hit a HoJ or a heal when I was in range, and it would insta-dismount me and cast the spell.
I leveled in dungeons, and people with pets had their pet indented and displayed under their own portrait and I could easily buff or heal it when the time came.
I will concede that these things may have been interface options that I had to check the box for them, though.