How do you handle overlapping starting skills from origin and career? I do not know official rules concerning this, so I am asking for house rules.

Example:

Rhia is a Schola Progenium adept.

Her origin grants her the skills Literacy, Speak Language (High Gothic) and Speak Language (Low Gothic). Her career also grants her Speak Language (Low Gothic) and Literacy. Does she end up having Literacy +10 and Low Gothic +10? In most of the cases of course it won't make a difference, but one day her life might depend on it. Did you already have such cases?

I'd personally consider giving them a cost reduction for another skill in their first rank to spend with their starting 400 XP instead.

No the overlap is just so that adepts who start out on alternate start scheme have access to the basic skills/talents. If you read the errata closely. You'll find they put all the starting skill/talents for all the classes into their 1st rank.

Overlap is just that: Overlapping. Not stacking.

The Low Gothic for the Schola (and some other IH homeworlds, IIRC) is probably an oversight as all careers provide Low Gothic while most homeworlds include the more exotic language skills.

I would generally tend to offer them something to compensate, since generally where their are cases of overlap the career + background combination make sense. So either another skill from the starting section of their career for 'free' or the ability to get the +10 when they reach a high enough rank without having to pay the exp (A sort of delayed bonus.) That being said I doubt any campaign is going to be imbalanced by early access to a +10 in low gothic.

Also I'm the type of person who would offer discounted purchasing of skills if the character had it as an atypical basic skill. (So pilot (Space craft is cheaper for void born etc))

There is no real reason to over "compinsation" to your player because they have an overlap skill, every class in the game will overlap now and then with it's starting skills from planet and package. It happens but DH already is built to handle it, you don't really need to do anything. It's not like they are being jipped ;D