Bear in mind, most of the information that follows is my interpriation of the Imperium. Not every last bit of it is totally canon.
Navigator Houses are varied. They divide themselves into rough collections: noble, common, and rogue. Noble Houses operate like royal families and deal like them. Common Houses are closer to guilds, they function like businesses. Rogues are highly suspect, bordering on hersey in many places, at odds with more upstanding Houses.
All Navigators are human but only in the sense that mutants with stable mutations are human. Like many things within the Imperium, mutants are grey. Useful, longterm, stable mutation is often allowed to pass by without burning, especially when it is useful. Navigators all develope the same basic mutation: a third eye on their forehead which allows them to "see" the warp.
As they age their bodies alter farther, generally becoming tall and thin with clawed hands. There is variation in this mutation but it is consider stable enough that it doesn't require purging (and besides: they need Navigators).
A Lord Captain who gets blackball by a Royal House is basically shut out. As much as the Royals might feud but they all recognise one another's nobility and one who snubs a Royal is not to be dealt with again. The Commons are businessmen who have alot of pride but respect coin far more. Rogues are a fairly random element.
Your old Nagivator is a member of a Royal House. Depending on what he tells his family, Captain Trask may find himself locked out of the Royal Navigator option.