You aren't going to starve with no money, thanks to your pension.
As to why you bought the weapon, the short answer is a series of criticals. If you like, I'll give you the details as to what happened, roll-wise.
The magistrates and leaders of the city might be mildly intrigued at you, but if you arrange a meeting, it would be best if you had an exact reason for involving them in particular, instead of just saying 'hi', so to speak. If you want to make contact with them more loosely, it would be best to do so at some kind of social event. Also, the more prestige you have, the easier it is to get access to people in important positions. With your condition being formally documented, it seems likely that your name will be more out there in the future.
Execute the plan, be patriotic enough to spy for our own country. Anything for better starting money.
You decide to ask Huan Zhang about finding more important duties than being a servant, with your need to make more money. He notices that you are armed, and looks amused for a moment.
(-1 favor with Huan Zhang.)
It turns out he knows someone who would be happy to have you run messages, which would pay similarily but take up less time than servant work, and only be minimally more risky. He also says that you could be asked to do more complicated jobs for extra pay, and you can start that next week.
However, he has just the thing for you in addition to that. There is a student clerk in the government quarter who has stolen an official seal, and is using that to authenticate forgeries. He asks if you'd be interested in trying to retrieve or destroy the seal, and perhaps collect information about who has bought the papers. If you manage to do that, he can pay you pretty well for it, say, 13 silver.
Also, he says that if you just need money in a hurry, he would be happy to float you a loan.
Do you say yes or no to each of these?
Week 5. Time available, no actions.
Assets and Abilities:
Prestige = 0
0 silver.
Ancient bronze short jian.
Allies:
Min Li, spirit reader, 2 prestige, 0 favors
Huan Zhang, diplomat, 2 prestige, 0 favor