Frustrated with static body fat %

1) You might want to lower your cardio and increase weight lifting. Could just be that you're not doing enough in the lifting department. I lift either 3x a week for about 40 mins each, or 4x a week for 30ish mins.

2) 1200 calories is not nearly enough to help fuel your workouts and minimize lean body mass losses. Set up a more reasonable goal, like 1lb or 0.5lbs/week. Also be sure you eat back your exercise calories if you are using the MFP method. If you've been losing weight in the last 3 months then you've probably lost some lean body mass.

3) You are not eating enough protein. What is your current weight? Eating your lean body mass in protein or multiplying your weight by 0.82 should give you an idea of how much protein you should eat daily.

I'd rec getting a food scale so you can be as accurate as possible with your intake. Only measure liquids, weigh everything else. Log daily. Notice any trends, increase or lower intake if you don't see any weight loss or see too much.

Cardio isn't required to lose weight, so do it if yu enjoy it I almost never do it personally. But as far as the deficit goes, MFP assigns 1200 to pretty much everyone who chooses 2lbs/week as their goal. What goals did you set up? Also, I'm a student and sit around most of the day, but if I use MFP activity then I need to select lightly active. Few people are actually sedentary.

Basically, if MFP says that without exercise you could maintain on 2200 calories, then a 1lb deficit should be around 1700 calories. This is without exercise again, so when you exercise you'd log and eat back at least half of those calories. So if your goal at the end of the day ends up being 1950 calories, you'd want to eat up to that or as close as you can. Don't create more of a deficit from the existing deficit!

Here are some of the main foods I get protein from:
Poultry, meat, fish, eggs, greek yogurt, cheese, cottage cheese, whey powder, sometimes PB. I often mix protein powder with baked goods or e.g. yogurt + fruit. But I do make a lot of meats.

Personally I think that everyone can make/find time to cook, it's all about your priorities. If it means making stuff in bulk once or twice a week, then that's fine. Or cooking really large dinners a few times a week and having leftovers. At your weight, 100g of protein would probably be enough for daily consumption.

You don't need a food scale, it's just way more accurate. But if you can get within the ballpark then it's okay. It's really quite easy to weigh food though, but not necessary. And you definitely don't need a specialized diet, other than just eating more protein.

Also looking more closely at your diary, I think that you could make a few other changes for improved accuracy without buying a food scale. 1) don't use generic entries (look for USDA entries instead for fresh ingredients), 2) don't use generic recipes (e.g. your PB&J is a generic entry - instead just log the bread and the PB and the jam that you are actually using).