Is it possible to become Thane of Falkreath without completing the main quests or the civil war quests?
Solution 1:
Windhelm requires you resolve the civil war one way or the other before becoming Thane or purchasing the house. Whiterun requires you complete the first couple of quests in the main quest chain. Falkreath has no such restrictions.
However, the first quest you have to do for the Jarl can be blocked if you have another variant of the Rare Gifts quest under the Miscellaneous section in your journal. If you do, complete it. If you don't, visit all the other possible quest givers, and if any of them offer you the quest, complete it, then check back with Siddgeir again. Repeat if necessary.
Solution 2:
I've been playing with console commands to try and get a fix to a hearthfire bug, and I think I may have figured out this problem. You can only have one Favor110 quest active at a time. Follow the above link. If you have any of the other Favor110 quests active, he will not speak with you. Make sure to complete (or skip) any of the other Rare Gifts quests and he will be available to give you quests to make you Thane.
Solution 3:
As for problems completing 3 quests to become Thane of Falkreath, it's not glitched, at least not completely. If you are like me, you are working on this later in the game and many of the people in the town have been killed off by one or more dragons that you've had to fight over Falkreath. So many of the suggestions people are giving don't work. The Farmer and his wife are dead or gone, same with the blacksmith and others. The "dropping stuff in front of the soldiers" trick doesn't work. I found that I had 2 of 3 quests completed to help citizens of Falkreath, and couldn't find a third to finish it off. It seemed I was at an impass. The quest to rescue Valdr (Hunter and Hunted) you get from Valga Vinicia, the tavern keeper of Dead Man's Drink, doesn't count for some strange reason. Neither do one or two others. I was about to give up and call it an unresolvable bug... then I realized that the citizens you need to help don't have to be in the town of Falkreath - they need to be within the larger region of Falkreath Hold. I eventually found Heri at Half-Moon Mill on the west side of Lake Ilinalta (NW of Falkreath) and chopped some wood for her. Voila, third quest finally completed! I am now Thane of Falkreath, but Jarl Siddgeir is a poohead. And no, you do not get the option to buy a house in Falkreath.