AFAIK the only situation that you can take damage and not take a BM is from losing units from a failed dangerous terrain test, because the DTT rule specifically notes that you don't take a BM for losing the unit(s).
So:
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Warhound A - does it get another Bm for the damage point from the collision?
Yes.
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Does it test again for a critical from that damage point?
We've generally played this as yes.
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Warhound B - does it get a shield or DC removed?
Come on now Chris, you know that you're being evil here.
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If a DC does it get a BM?
Yes.
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Does it then roll to see if that damage point causes a critical?
Yes.
I once had two Warhounds that repeatedly headbutted each other to death, after one of them took a single damage point from a humble lascannon.
And here's a relevant quote from the rulebook:
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...any hit on a war engine (no matter how it was inflicted) has a chance of causing critical damage...