Interesting topic. My take:

The disapproving Captain - He goes tomorrow.
If he was stupid enough to voice his displeasure,to leave him alive would only serve to make him the focal point for other dissatisfied members who would now know they had an ally for a possible coup.
A new Boss has to establish the respect he is entitled to from day one. Also,the remaining members will feel secure in their respective roles,knowing that their survival means that the Boss has settled all scores,and everyone starts with a clean slate.

I'm assuming that as a Family Boss,I was now seated on the Commission,therefore the situation involving a plot against another Boss would be decided on a vote. After hearing the case made by the person who wants to whack the Boss I can vote without taking a side,but rather by deciding what is best for the Organization as a whole'

I go to jail - I name an acting Boss who is in charge of day - to - day activities with the assistance of the Consigliere. Any major decisions - murders, Inter-Family matters,etc. will be transmitted to me through my trusted Family attorney during his regular (and un-monitored) visits.

Rackets - the usual_ Gambling,loansharking,unions,construction (including bid rigging) ,hijacking, plus some stock frauds,bustouts,bars,restaurant and strip club ownership, in General the usual. If you deal drugs,you do it on you're own. Get caught,you go.

Structure - Soldiers report to Captains,Captains to the Underboss,Underboss to me. There may be some circumstances under which ,a select Capo or two,may approach me directly.
The Consigliere's position is as a neutral party. His main function will be to advise me, but more importantly, he serves as a buffer to the Family members,both to give them a safe place to address concerns that they may have,and also to serve as a layer of protection from the whims of a capricious Boss.

Money flows upward,but everyone is assessed a fair split. Associates split 50/50 with the Soldier they are under,Soldiers split 50/50 with their Capos,Capos kick up 10% to the Boss (Capos have many Soldiers under them,so 10% is a good bit of money). Separate arrangements will be made foe the Underboss and Consigliere depending on whatever businesses or crew they are running.