How to set up something to trigger after the set up time.
I suggest using BoojamSnark's mapping resource pack to get the basic entities for whatever gamemode you do:
http://forums.tf2maps.net/showthread.php?t=4674
In the default set of entities, you'll see a
team_round_timer. This is the entity you'll use to fire things that happen after setup, by adding something like this to the outputs:
OnSetupFinished -> <name of trigger/relay/etc> -> Trigger > 0.00
How to rig/animate/set up an explosion of rocks.
Rigging and animating an explosion of rocks is a very complicated topic. It requires that you understand not only how to create models, but how to rig bones, weightmap, keyframe animate or run a simulation, etc and compile the models with the appropriate sequences. That's a very big topic in and of itself, and without knowing your current level of experience it'd be pointless to start talking about.
You might be able to create a very basic explosion with
func_breakable, but it won't look nearly as nice and polished as you see with the payload explosions in game. It would however be a good start if you just want to learn how everything works together.
You'll also want to use an
info_particle_system and an appropriate existing particle to create the explosion, dust, and so forth. Save that for last though, after you've figured out how to work with all the rest of the entities -- you'll have to start TF2 in "tools mode" to preview the particles, and that, too, is a whole different topic of its own. Once you've found a particle system you like though it's just a case of triggering the info_particle_system same as anything else.
How to make the explosion hurt close players/buildings.
The entity you'll want to use is
trigger_hurt. Start by creating a brush with the tools/trigger texture. With the brush selected (and only the brush), hit control-T to turn it into a brush-based entity. From the dropdown, choose trigger_hurt. The link will explain a lot of the settings.
How to set up sounds to play with the explosion.
For this, you'll want to use an
ambient_generic. You can browse for a sound from the entity in Hammer. This entity should be named, too, and you'll trigger it as above.
Making cinematics like this can be quite complicated and involved. You have to keep track of the timing of everything, animate props, etc and so forth. I get the impression from your post that you're relatively new to Hammer, so I strongly recommend getting familiar with how the entity system logic works before attempting a cinematic.