Regarding the Bishop wearing a dalmatic under the chasuble, that is part of a Bishop's full pontifical vesture for a Pontifical High Mass. At a Pontifical High Mass a Bishop wears: buskins, sandals, amice, alb, cincture, pectoral cross, stole, tunic, dalmatic, gloves, chasuble, and miter, and carries the crozier.
For a Pontifical Requiem Mass, as well as for Good Friday (since it's "kind of" a Requiem Mass) a Bishop does NOT wear the buskins, sandals, or gloves, nor does he carry the crozier.
As far as your question about the Veneration of the Cross, I too have seen it done both ways. I've been to several different churches for the pre-55 Holy Week and it seems to be a function of both how big the church and sanctuary are, as well as the number of faithful there.
In larger churches they tend to just bring a crucifix to the Communion Rail and the people come up to kiss it pretty much as they come up when receiving Holy Communion at the rail. It's been a couple years since I was last at Saint Gertrude's for Holy Week but I believe that is what they do for the Veneration of the Cross by the faithful.
In smaller churches, like my own chapel and several others I've been to, they roll the purple carpet all the way down the nave, and the faithful take their shoes off and do the three double genuflections just like the clergy and servers do.
Regarding the broad stole, I'm not sure of the purpose or meaning, but as far as its function it is worn by the Deacon from the Gospel of the Mass until Communion time, after which he puts the folded chasuble back on.
Similarly to this, at a Solemn Mass when folded chasubles are worn the subdeacon takes his folded chasuble off to sing the Epistle, although he does not put something else on as the Deacon does in the case of the broad stole. The subdeacon also puts his folded chasuble back on much sooner than the Deacon does.
I'm not sure of the symbolism of the AP and the Deacon sitting on the altar steps on Good Friday, although I have been impressed by that myself too when I've seen it done.