I have in multiple versions made more than enough money to finish the entire debt with little to no difficulty using the default start option, while using what is supposedly the slower method of making money (pure gathering workforce). The first time I did so it was a close call around the day 50 payment because I didn't have a clear idea of how to progress along that path yet, but the latter few times I have finished building every payment with weeks to spare.
I have not fully tried in the latest version yet, but I have made the 1k for the first payment in less then one week, so 3k more should have been easy by that due date. The main thing to note about trying to actually pay the debt is you should try to focus either full gathering, or full combat from before you even make your characters, the quicker you can get the rhythm the easier a time you will have. An important note; anyone you send to a dungeon, combat encounter, or noticeboard quest will not do whatever job you've given them at the mansion until they return.
As for the quests they are a bit difficult in the first couple weeks no argument from me.
The quest requirements can be anything from the tier you set them to for that faction, though they do default to the easiest tier of quests. You might not have the infrastructure to complete all or even any of the quests for a week or two if they randomly pick craft tools/accessories before you have the smith/tailoring upgrades, however you can buy items to fulfil the requests if you can find them in the market, the market stocks change daily, and some of the places you can travel to (mainly the locations that are only one 'turn' away) have markets of their own that also change stock daily.
The item turn in quests can be completed with things bought from the market usually for more than it costs to buy them as long as the reward is only gold and rep, if you have higher charm the rewards from quest will also increase.