Just a thought a friend of mine brought up while working on a Warforged character: since a shield bash attack theoretically has about the same movements as a Warforged slam attack, shouldn't you be able to add your Slam damage to a shield bash? I mean, sure the shield spikes hurt already, but when the force behind it is supplied by an angry 270+lb magical robot, it's bound to be more powerful than an average human carrying equal weight, right?
No, they are separate attacks. A Slam isn’t actually hitting something with your arm so much as body-slamming it, at least for Medium creatures.
Even if you wanted to say they were the same action, the stacking rules would say that then you just deal whichever has the greater damage; they would not stack.
The only way I’m aware of to do this kind of combination is the Beast Strike feat from Dragon magazine, which combines a Slam (or Claw) attack with an Unarmed Strike. Combined with an aptitude shield (aptitude is a special weapon property from Tome of Battle), you could use the shield instead of an Unarmed Strike. But that’s the only way I know of to achieve it.
As for a houserule, a feat à la Beast Strike but for shields+slams wouldn’t be unreasonable; actually, it’d be kind of on the weaker side.
No, for the same reason running faster doesn't increase your damage on a charge.
A warforged's slam is essentially just a punch that does more damage because its fists are made of metal instead of flesh. Hitting with a shield is no more beneficial. Rules-wise, a slam and a shield bash are just two separate attacks you can't combine.