200 EUR will get you a shared flat with several roommates, who would in all likelihood be university students. That's a bit low for accommodation funds, you need to calculate spending money on top of that if you want to live on your own at all. Let alone in furnished accommodation with an Einbauküche. Check out immobilienscout24.de if your German is good enough. I just browsed around and found some offers in Connewitz for 280 a month. It's a bit out of the way and insanely tiny, but it seems do-able.
I hope this link works
If you need to send 500 EUR a month back, you will have 700 EUR including your housing allowance. That's... a very tight budget. Are you sure you need to send all that money back? Because your pay just isn't high enough to lose such a large chunk of it. That's going to be a problem. You should VERY seriously think about this before you commit to this job! Remember that you have to pay for things such as insurance, transportation, communication, food, toiletries, and any entertainment. You will be living on a poor student's budget, so no big expenses like travelling around the country.
On the upside, if you're ready to face any weather, you can get almost anywhere in this city by bike, especially in the summer months. Depends a bit on how presentable you have to look at your place of employment, though. If you shop frugally at places like Aldi or the local farmer's market, you can eat healthily on a budget. But remember you have to eat lunch at your work, too. Finding friends.. really depends on your age, hobbies, etc. If your work colleagues are of the stiff sort, prepare to make some effort to find friends at first. Germans are a bit more reserved than some other nations and don't necessarily invite strangers into their circle right away. Don't take this as rejection but see it as a challenge. Don't wait to be invited, but invite people yourself, basically.
Landlords won't mind renting to single women.
Accents... that will undeniably be hard. Even Germans from outside Saxony can struggle with this. Luckily, it's mostly older people who speak with a really strong accent, and most others are able to switch to a more intelligible form of Hochdeutsch.
There are some neonazi problems in Leipzig, but it's nothing out of control at all. Avoid moving to Lindenau or Reudnitz, stick to Südvorstadt, maybe Schleußig or anywhere near the city center, those are all very safe areas.
Can't help you with the footy, sorry.