I under ate by 4000 calories

Don't eat UNDER your BMR!

On and last week I ate nearly 4000 calories under target

With there only being 7 days in the week, and your goal being 1300 calories per day, you're saying that you only ate an average of 729 calories per day?

ETA: What do you consider a proper meal if you're eating just over 700 calories for the whole day?

Eating so little you stand to lose a lot muscle mass. Over a long time this can cause a decreased metabolism as muscle is metabolically active tissue.

This means that your maintenance calories will be lower, meaning it will be easier to regain weight once you start eating properly again.

I've looked back a couple of days in your diary. A small plain jacket potato and some packet pasta and cheese sauce are not proper meals for a whole day. Together they may constitue one meal.

Seriously, it's not difficult to eat more. Put some butter on your jacket potato, eat an avocado, a handful of nuts, some full fat milk, cheddar cheese. Avoid anything with the words 'low fat', 'light', 'diet', 'Weight Watchers' on the label. These small changes can easily get you up to 1500 cals per day.

I've looked at your diary and notice you also rarely eat breakfast..... that would help. Currently you are UNDEReating....

If you find that you're not hungry and you just can't eat more, then drink it. Get a quality protein supplement or meal replacement shake and drink enough of it to reach your caloric goal.

Less than 1200 a day is going to cause you health problems and cause you issues in losing weight, maintaining or being healthy. I'm genuinely not trying to be mean, only to answer honestly. It looks like you need help discovering what healthy meals look like and consist of. On top of not eating enough calories, your meals also seem to be nutritionally lacking.

If you are unable to do so on your own, see a doctor who can help you figure out some balanced meal ideas. If you want to be successful here, treating your body well and feeding it well is absolutely mandatory. Good luck, look for healthy foods and then eat until you get right up to your calorie limit every single day

My question is this.
Will this slow my metabolism down and cause me weight loss problems?

Yes

in the short term, even if you're not generally feeling hungry on this amount of food, that's because your appetite can shut down, then suddenly come back with avengence, leading to binge eating. Another possibility (not everyone's body works exactly the same in this respect) is that you'll be constantly battling against hunger and the urge to overeat. Whichever way your body responds, the result tends to be getting locked into a cycle of undereating and rebound overeating, which leads to fat gain from the overeating (or even binge eating) that goes with this.

in the not quite so short term, there's a risk of losing lean body mass as your body metabolises your muscles to try to make it through the food shortage (as far as your body's concerned, that's the only reason why you wouldn't be eating enough) - this has two effects that the body finds desirable for surviving food shortages - 1. the muscle cells that were metabolised no longer need energy to keep them alive, so your basal metabolic rate is lowered, and 2. burning muscle cells means it doesn't have to burn as much fat.... trying to make your fat stores last as long as possible is your body's aim during a food shortage. If you consider that while this is going on, the person's likely to be in a cycle of excessive restriction and binge eating... during the excessive restriction phase the body's going to be burning muscle cells for energy and trying to minimise the amount of fat that's being burned, then in the overeating/binge eating phases, the body's going to store all the excess as fat.......... the result is the body fat percentage going up or staying the same, rather than going down.

What most people want when they diet is a lower body fat percentage, i.e. keeping the lean tissue and getting rid of some of the fat.... eating too little does not achieve this for the reasons I've outlined. What you need to do to lower your body fat percentage is 1. feed your body properly, the deficit for fat loss should be small. If you only have a little fat to lose (i.e.you're already in the healthy BMI range for your height or you're close to it), then your goal should be 0.5lb/week. If you have a lot to lose, then aim for 1-2lb a week max. Only if you've got hundreds of pounds to lose should you aim for faster weight loss than that (the more fat you have the easier it is to lose without losing muscle etc with it). You also need to do exercise that works the muscles hard, e..g weight lifting/strength training, plus ensure adequate protein intake. Changing your focus from scale weight to body fat percentage really helps to get everything into perspective and understand why things like strength training, eating properly, and only having a very small deficit is so important, and why undereating sabotages your progress so much.

You don't have to eat breakfast to get enough calories not everyone eats breakfast and they don't all eat 750 calories a day. On the diet you have you will not be getting enough vitamins and minerals or Macros for your body to function properly, you will ultimately not just affect your metabolism but your immune system and health. Do you exercise, that may give your appetite a boost if you don't want to feel like you are forcing yourself to eat, to echo other people, go for healthy fats, to give you a calorie boost, you don't have to eat more just eat the right sort.

Yeah, 4000 calories under target may not be the best. for me, i would find it a very sudden change of habit, and I may go back to my bad ways. Setitng a target of 1 or 2 lb loss per week is great, unless you weight like 500 lbs in which case you should be talking to specialists.

One pound per week is APPROXIMATELY 500 calories less per day. If I was a healthy 20 yo male with a government suggested standard of 2300 calories to maintain my 160lbs, then a daily intake of 1800 cals should (not guaranteed) make me lose 1 lb per week. That is 3500 cals less per week.

I want to lose 2 lbs per week. so, I should drop to 1300 cals per day I will definitely feel less energy and now i should more closely monitor that I get the necessary daily protein, carbs, and fats

Now, let's say I go 4000 cals under my weekly target. That is 570 LESS per day. Now I am at 1300-570=730 cals per day. That 730 is damn few to maintain activities of daily living, like staying awake during commute at rush hour, or getting through laundry, cleaning, and repairing the lawnmower.