Started running, putting on weight..

first of all... why are you eating extra calories? Exercise is supposed to burn calories.... you eat your basic cals per day, not eat extra to make up for the exercise, and someone else said, you may be overcalculating how much you are burning.
I can tell you right now... MFP is NOT accurate for exercise cals, ridiculously over generous.
I can see plain as day why you are gaining.... STOP eating your exercise cals. End of story.

I never eat the calories I burn during exercise! I hate that they add them on there. I consider those my weight loss calories. I always hear that you have to burn more than your eat to lose weight. If I eat my exercise calories, how can I loss weight? That's just how I see it. I know a lot of people do eat them. It's a personal thing.

With respect, it sounds like you are both misunderstanding how Myfitnesspal works. It gives a calorie goal with a calorie deficit already built into it, based on the information you entered when you signed up. MFP asks about your daily activity level, but does not include planned exercise or workouts like going to the gym, or running. It includes the activity from your normal day to day activities like your job, or household chores, or shopping etc. How active you are in general. That forms the basis of the calorie goal you get, and it is based on the assumption that any workouts you do, you log those and eat back the extra calories. Otherwise, MFP would have included all planned exercise and would have given you a higher calorie goal to start with. With the calorie goal MFP gives you, you can lose weight with no formal exercise. Of course, exercise is beneficial for lots of reasons, but that's besides the point. The vast majority of your daily calorie burn comes from your body's normal processes that keep you alive, and your normal daily activities. Those are really your "weight loss calories".

If, for example, you tell MFP you are sedentary, and then you go running 3 times a week, MFP will have given you a goal based on you being sedentary, and any additional exercise will be making your calorie deficit bigger. Sounds good, but having too large of a calorie deficit can be unhealthy and counter-productive over time. You risk losing far more lean mass than you would do otherwise, and you also risk messing up your hormones. This is especially true the closer you are to a healthy weight.

Now, a lot of people on MFP choose to customise their calorie goal to include all the activity and exercise they do. They don't "eat back" their exercise calories, but they end up with a larger calorie goal to start with.

It is a "personal thing" how big a calorie deficit you ultimately choose to have, some people decide to eat 500 calories a day and that's their choice. Doesn't mean it's a good idea. Understanding how MFP works is a good start, and giving blanket advice to stop eating exercise calories back is a really bad idea. In general, people who are obese and have larger amounts of fat stored can "get away with" large calorie deficits more than people who are closer to a healthy weight.

I started running 3x a week the last 2 weeks and my weight loss stopped after week 1 and now after week 2 i've put on a half a kilogram.

I'm using the a running app which allows me an extra 300 calories on the running days. Is it better just to focus more on my diet? or not add the running calories?

why, do you think you're not focusing enough on your diet?

are you running on an incline? I put on a little muscle weight when I run but there are hills where I am ...

From what I've heard a lot of the weight you lose in the first week is often water weight and the loss slows a bit for a couple of weeks and then picks up and you start to lose a little more steadily. I don't eat my calories back on days that I run, and eat back most of what I do on the days (mostly just extra protein) on days that I strength train.