I feel like I am eating so much more than I used to... Is that normal?

As long as you're over 1200, I'd say work on your logging first. Logging is more complicated than it looks, so you could be eating more than you think. (In which case, eating even more is not your best choice, since you say you're satisfied.)

For example, you list your cereal in cups. Cereal is a good one to weigh, as it can settle a lot. Fruit too. (Although at a quick glance, your log doesn't look too bad to me.)

Then... yes and no. If you're under target by a bit, I wouldn't worry about it. If you're under by a decent amount, and regularly, then maybe you can eat over target sometimes. (For parties, holidays, events, dates, whatever -- treats.) Just make it balance out over time.

Otherwise, it's good to hit your target. This is set for a healthy rate of weight loss. That said, at 300 or so, you could healthily lose quicker than 2 lbs a week IF you want to and IF you feel okay doing this. (Many people say about 1% of body weight, which would be about 3 lbs a week, right now.)

I'd also like to mention that what you told MFP you would be working out at has no bearing on your calorie target. (Which I found confusing at first.) You could put 0 exercise or all day every day and your calorie target would be the same. It is when you log ACTUAL exercise in the exercise log that it matters -- and then you get the calories back to eat. You get them back to eat to help ensure you get the targeted healthy loss. So if 1580 is what you eat to lose 2 lbs a week, that means that your body burns 2580 before exercise. If you burn another 500, that's 3080... but if you then still only eat 1580, you're creating a bigger-than-planned deficit, and faster weight loss. (Which again... for you, at your current weight, might be okay. But so is eating more if you feel you need to, to stick to the 2 lb plan.)

Finally, you might want to stick with eating back about 50% of exercise calories, if you choose, in the beginning. This is a safe spot that will guard against overestimation and maybe give you a bit of a buffer if you are logging inaccurately sometimes. You can watch your progress over a month or two and adjust accordingly (to eat more or less of them).

I agree with PP that logging accurately is a good idea. There's a very real chance that you are off by just a bit on some measurements and eating more than you think. Not a big deal right now, but accurate tracking could be the difference between showing that you are under calories and showing that you are eating enough.

Other than that, FAT! IMHO, you need more fat. If you eat a low fat diet long term, you could be more apt to experience gall bladder issues in the future. Fat also helps keep your hair and skin healthy and helps keep things moving. If you don't feel like you need more volume, add more fat. Instead of fat free salad dressing, use some with fat in it. A lot of the nutrients in vegetables are fat soluble, so if you eat a salad with fat free dressing and extremely low fat meat you are missing out on absorbing some of the vitamins and nutrients. Plus, adding a little fat is a good way to add calories without adding volume. Two tablespoons of regular salad dressing is the same volume as two tablespoons of fat free.

Just make sure you are eating enough to feel full and sustainable, try not to under consume what it tells you for 2 lb a week loss.

I started at 333 lbs, after 11 weeks I am down to 310. That is an average of 2.09 loss per week. I have been very physically active. I eat back half the calories given to me for exercise and weight and carefully measure all my intake. It goes to show that for me at least the numbers mfp provides are right on.

If you are not meeting your calories now just have some nuts, a scoop of peanut butter, some extra olive oil in your cooking...etc. It always seems easy to cut calories at first, but over time a slower weight loss with a healthy sustainable diet that has enough calories is going to create better habits.