I am of the opinion that the best way would be to fix eating habits and the daily diet, with exercise as the supporting pillar.

In terms of weight loss, a good diet can help compensate for a lack of exercise in most cases. But exercise usually cannot fix a bad diet.

Get proper nutrition in. Meet your daily protein intake. Don't starve yourself, it will make things worse.
Get an exercise routine going. Weight training is mandatory.
Stick to it. Consistency wins.

Good luck.

How do you know if you don't have enough vitamins and minerals?

Food court diet is not necessarily worse than home cooked meals. Home cooked meals is not necessarily 'healthier'.
You could make an argument that food court meals has higher sodium on average. It comes down to your choice of meals. So look at it from that perspective.

If you eat the same meal week in week out, then you probably need some variability. Vary your vegetables; get green leafy ones as well as the ones that are not. Vary your protein; chicken, fish, beef, eggs.
By varying your diet, you cover a wider spectrum of nutrition.

If you don't have enough vitamins and minerals, you start showing deficiency symptoms pertaining to the specific nutrient.
In general, you do not need multivitamins. Multivits have been marketted as a catch-all, more people take it with no benefit as compared to those who do.

In summary, don't spend too much time thinking about it and scare yourself into doing something just to 'cover your bases'.
Vary your diet. If you have a deficiency, fix it by introducing foods into your diet rather than relying on multivits.

Happens to me sometimes.
Take a slow digesting protein blend before bed to fix it.

You need to expand your understanding on what a caloric deficit is to be able to calculate the facors around it.

First you need your caloric maintenance. Which is the amount of calories your body needs to sustain bodily function and retain current weight. Let's assume this is 1500 for this explanation, please calculate yours.

Next is the caloric intake. Yours is at 1250. So you are 250 calories below your maintenance, which translates to weight loss over a period of time.
But what if you exercise? Assuming your caloric maintenance is 1500 normally without exercise, then 400 calories worth of exercise will bring that number up to 1900 calories for the day.
Assuming you are still on 1250 caloric intake, your deficit now is 650 calories. If you want tor eain your 250 caloric deficit, it means you can increase your intake from 1250 to 1650 without compromising your weight loss.

As with everything, do this gradually and watch your macronutritional needs to prevent specific deficiencies from cropping up.

Crash diet is good if you absolutely need to lose a lot of weight in a short period of time. Like if your life is on the line in a Saw movie.

Apart from that I would not advocate it.
People need to realize losing weight and being healthy aren't one and the same. Unless a person is obese, then yes it goes hand in hand. But to those who are not obese, the primary reason to lose weight is for asthetics. There is always a price to pay for that.

You can go on meal replacement programs and drop a lot of weight, yes. Can a person sustain it for 10 - 20 years? Maybe not.
The main problem with consumers of crash diet meal replacements are their exercise is usually zero and their diet is full of holes. Their only focus is weight reduction. They don't have much muscle mass to lose in the first place. So in the long term, they become quite fragile. A innocuous fall might break bones because bone density has fallen. Health problems might start to crop up. We all pay the price of our decisions.

Which is why I ask people going into this for the first time to get their priorities straight. Is it primarily to lose weight, or to get fit & healthy?
The easy way is to look for products which we really don't need.