I think this happens because minecarts are entities, like mobs.
Confirmed in 1.7.4.
Did you alert them of your presence before you became invisible?
In 1.4.5, Infant Zombies weren't official. Only mods could spawn them. These days, they are natural and have sounds.
You are either using a mod, using creative or lying.
No, there's no absolute way it can be server lag. I'm sure that this glitch has been around since before the LAN button was introduced, even on singleplayer!
Confirmed to be in 13w48b. Happens when the top is set on fire, it appears to be a corner wall for a few seconds.
This still happens with Blazes in 1.7.2.
This glitch still exists, even in the most recent version, as of what I know. I'm not a Mojang developer, but I can tell it's a hitbox glitch. The mobs can't be hit until the block they're in is broken.
You could be either hearing things or using sound packs.