First of all, I haven't played Milan and Venice for a long time. I found this info when using Forum Search, looking data files and I add some bits I remember about them.

1) Morale - What exactly is the numerical bonus to morale provided by the Carroccio Standard? And what is the ultimate range of the Carroccio's morale effects? Additionally, is there a morale penalty administered upon the loss of a Standard, and if so, what is the numerical value of this penalty?
I'm not sure how much is the exact bonus but Carroccio have attribute called standard in edu file. I think this attribute is hardcoded and unfortunately I don't know how much bonus it gives. Try asking in the mod forum in here or in twc if you want to know the exact number. There is no morale penalty if Standard is lost but if it is destroyed you will loose morale bonus it gives.

2)Spearmen Attributes - I'm well-aware that Carroccio standards are pushed by spearmen that never rout, even in the face of suicidal odds. My question is pertains to how they operate in combat: Spears normally get bonuses against cavalry charges, but do they lose these bonuses while pushing the cart? Can a Carroccio Standard bodyguard rout if separated (i.e. ~ no longer pushing) the Standard?
Carroccio have lock_morale on the stat_mental line. This must be the reason why Carroccio guards fight to the death. They will receive spear bonus even when they push the cart. And they will not rout when separated from the Standard.
Check this:https://forums.totalwar.org/vb/showt...occio+standard

3) Deployment - What is the ideal tactical deployment of the Carroccio Standard? Common practice seems to have the Carroccio immediately behind the center of the line of Spearmen. But because spear and pike militia generally suffer from low morale figures and an extreme vulnerability to flank attacks, is there any benefit to placing a Carroccio standard directly behind each of the flank-protecting spears or pikes (i.e. ~ the left-most and right-most units of a spear or pike front line)?
I think this part have been answered already in this thread.

4) Number - How many Carroccio Standards should be employed on the battlefield at any given time? (I'm curious about whether the benefits of a second Standard outweigh the costs or not.)
Depends against who you are fighting. From older threads I read that they are very good against Mongols if you have to defend your cities. But about 2-3 would be more than enough. Also, they are pretty cheap (at least in Vanilla game).

5) Finally, under what conditions is there a benefit to taking a Carroccio Standard into a multiplayer skirmish?
Since I don't play MP then I can't answer that question.

I do suggest you to use Forum Search option and check those older threads yourself. You might find something I missed.

Hope this helped you a bit.