1. Do I need fuel management? If so, then what should I use?
Yes, I would recommend a standalone, if you don't have the money for a new AEM or MoTech, Look for a good used one. Or even a cheaper option is a Piggy back ecu they are a cost effective option if you don't have a huge budget to manage your fuel and timing needs. A MAP ECU Ver.1 or Ver.2 you can get used for about 150 - 300 bucks or cheaper in my honest opinion its much better than an Apexi SAFC or HKS SAFR. Its mych easier to use. I'd recommend the MAP ECU for a budget.
2. Will my air/fuel ratio be way off with the turbo even with 24# mustang injectors?
You need a Wideband sir. An AEM wideband is about 200 bucks new Im sure you could snag a used one for 100 bucks ish. Make sure your boosting safely and staying on the safe side of detonation especially if you are going to be non-intercooled your charge will be HOT as it is this will lead to high cylinder temps. Wouldn't surprise me if you need to go one heat range colder on your plugs to keep from breaking up under boost. Wideband is a requirement hands down.
4. Do I need to run a wastegate/bov?
Both are required, Wastegate regulates boost pressure, There are two types internally gated turbos are simple there is no extra welding for a flange and dump tube like there will be for an externally gated turbo. In my opinion an external gate will be better in terms of reliable boost levels. Internally gates turbos especially the ebay ones have bad quality gates and tend to boost creep, Or they will start to open too early and boost will come on super slow. A BOV will keep your turbo from surging, Its argued that surge will not kill a turbo in the short term but in my opinion it is required for reliability.
5. Will I need to retard the timing? If yes then what would the best way to do so? MSD?
Timing retard is a good idea with an NA-T set up at elevated boost levels for sure as the ecu was not designed to see positive pressure there for it dose not really know how to deal with it. Going back to your First question timing retard is a feature you will find in a standalone ecu, MSD can help you out as well for the price of an additional component.
6. Based on all of these factors, how much would I be in the hole money wise? I'm already nearing $500 and I am on a budget and this IS my dd...
Take all this with a grain of sault, Remember
You can only pick two brother, Better to save your paper and collect the required parts of good quality than to slap a kit together just to have a turbo ZJ tomorrow and be replacing parts in the future.