In Quest 8, The Trapped Ruins, the Overlord is granted 6 cards to start instead of 3. We are at "Hero Level" 5 so, according to the chart on Page 1 of the quest guide, the Overlord starts with an additional 4 cards. This makes the total 10. Since the Overlord can never have more than 8 cards in his/her hand do the additional 2 cards get shuffled back into the deck or are they considered "discards" and allow the Overlord to collect threat tokens?

The OL draws 10 cards then discards down to 8 (and collects threat for the discarded cards).

During the game, if the OL has 8 cards at the start of his turn, he still draws card and discards, doesn´t he? Meaning his hand limit can be exceeded while drawing, as soon as he discards down do it immediately after drawing.

I think so. That's certainly how we've always played it.