Can’t become Thane of Falkreath
Solution 1:
At this page there is a list of quests available in Falkreath which can help you to become a Thane.
The most easy ones in my opinion:
- Deliver Berit's Ashes to Runil
- Find Runil's Journal inside a random dungeon
- Get paid to gather crops
Then there is still the quest where you steal the Private Letter for Dengeir. So in total there are 5 quests, with Hert dead, that is still 4 quests left to help you become a Thane.
Also investing gold in the shops counts toward this, which makes it really easy for you with 100k in your pocket.
So check your quest journal and see which quests you haven't done yet. (I think crops and wood chopping is not listed)