Humanity is frequently at risk when performing Rites:

Only check for Humanity gain from Banish if Humanity < Power.

Do Humanity Check/Gain rolls get the usual role-playing/story/tactic bonuses and if so how?

They can. However, the severity of an action does not apply as a penalty for a Humanity check -- depending on the game's definition of Humanity, being rude to someone might incur a check... so might killing, raping, and butchering them (in that or any other order), and each check requires the same type of roll. [1]

Is there any way to earn bonus dice on the Humanity Check portion of the rituals?

Yes, but it wouldn't be based on a rollover from victories on the previous ritual rolls; it would have to be based on some other action relevant to Humanity in a positive way that was also relevant to the ritual. [2]

When do you get a Humanity Gain roll?

When you perform the action that merits Humanity gain. Actions to enable you to take actions that merit Humanity gain do not count.