The title says it all. When should I use pusha instead of push ..., push ... - I mean, when pusha gets faster than a couple of push instructions?

That depends upon so many factors that we can't know the answer.

My guess is that for modern CPUs it makes no difference at all. And any difference it might make would likely be unmeasurable except in very specific circumstances.

Essentially, don't worry about it. If you have to ask then that means you can't perceive the difference, if any, anyway.

Hard to say - pusha would in first save code space and might save execution time as well as there is only one instruction to read but do to pipelining this might be without noticeable effect. Anyway it uses more stack space so if you don't need to save all registers it is better to select them.