Can any projectiles/abilities enter the hero's spawn room?

You yourself cannot enter the zone, however anything else can, so bullets, bombs etc will all enter the room. The only way in is at the end of the game, on a point capture map, is to get trapped between the closing door and the room, and you will glitch in. It's also worth noting that if they're inside the healing zone of their spawn (the area where health regenerates rapidly), then you cannot damage then or effect them in any way.

For Junkrat, you can throw his traps and mines in there, however the trap will not trigger, and the mine will only effect enemies outside the spawn area. Di.Va cannot enter the room at all, however I will carry out vigorous testing when I get home and compile an exact list of what can/can't go into the room and how it behaves.

Genji: Shuriken will enter enemy spawn, abilities will not allow him to get into spawn.

McCree: Flashbangs can enter spawn, but will not blind the enemy, his ult (Deadeye) will target enemies in spawn with the red skull, however they will not die.

Phara: Rockets, ultimate and concussion mine will all enter spawn, but will not effect enemies inside it.

Reaper: Cannot wraith form or teleport into spawn. His ultimate effect does pass into the enemy spawn, however will not deal damage

Soldier 76: Helix Rockets, and healing aura will all enter spawn. His ult will target enemies in spawn.

Sombra: Her translocation just bounces off the spawn, and she cannot target anyone inside for hacking, and her EMP does not hack anyone inside spawn.

Tracer: Cannot jump into spawn, and her pulse bomb can enter spawn, and stick to enemies inside. It will only deal damage if they are outside however.

Basion: His ult, sentry and mobile configuration are all able to shoot into spawn.

Hanzo: All arrows, including ult ones will pass into spawn

Junkrat: bombs, mines and traps can all be thrown into spawn. The RIP-Tire cannot enter spawn, and cannot even climb up the entrance to it.

Mei: Both icicles and endothermic blaster can enter spawn, however they will not slow an enemy. Her wall cannot be used to force her into spawn, and her ult can be thrown into spawn, but can still effect players outside.

Torbjorn: His can fire into the enemy spawn, and the turret will target enemies in spawn. He can also throw armour packs into the enemy spawn too.

Widowmaker: Can hook into enemy spawn, but will not be pulled through the barrier. Her venom mine will land inside an enemy spawn but not be triggered.

D.Va: Can fire and use defense matrix into spawn, cannot boost into spawn, and her exploding mech will also not enter spawn when boosted at it.

Orisa: Can fire her shield to deploy into an enemy spawn, and can suck enemies back into their spawn, however she cannot suck anyone already in the spawn.

Reinhardt: He can fire strike and ult into enemy spawn.

Roadhog: Can fire into enemy spawn, but cannot hook enemies out of it

Winston: Cannot effect enemies in spawn with primal rage, can fire into spawn, and can place shield so it enters spawn

Zarya: Can fire into spawn both ways. Her ult, if fired into spawn, will only attract enemies outside of spawn (so if they enter spawn being dragged into it, they will stop being dragged)

Ana: Can fire into spawn, cannot effect enemies in spawn

Lucio: Can fire into spawn.

Mercy: Same old

Symmetra: Can fire into spawn, and even effect items inside spawn, but cannot effect players. Turrets and ultimate cannot be placed in spawn, or on the primary door leading out of it.

Zenyatta: Cannot discord enemies in spawn, can fire into spawn

All these were done on skirmish on a point capture map.