Why do you think that Sir T isn't disinterested in taking Fanny in or that Darcy isn't disinterested in saving Lydia.

Im not 100% sure about Henry in relation to William. I think that it is mostly done for the sake of trying to attract Fanny, but he may have a small desire to do soemthing useful and to help out a young man whom he recognises to be very worthwhile...
Generally speaking I'd say that most of H's actions are "interested"... ie that he's doing them pretty much most of the time wtih the idea of getting soemthing out of them, such as Fanny's affection. But possibly he's BEGINNING to move towards doing things out of a genuine desire to do good... and gradually if he had kept up doing that, the habit woudl have formed...
But as for Darcy and SIr T... I dont see waht D gets out of helping Lydia when he does his best to make sure that Eliz does not get to hear of it... and refuses any thanks from the Gardiners... and as for Sir T.. what does he gain through helping the Prices and particularly Fanny? True that once she came thtere, she gradually DID start to become a "lady in wating" for Lady B and a gofer for Mrs N... but that wasn't how it started.. He meant to give her a decnet education, help her to be on some kind of eqaulity with his daughters and possibly help her towards finding a husband.. and if she didn't he says that he intended to make sure that she had a suitable provision for a "gentlewoman"... and he helps out with the other Prices as well.. Its hard to see what he gets in materail terms in return for this.. Even if F HAS become a companion to Lady B.. he could get a real "paid companion" for very little more money...