FACTS:
I go to university in Edinburgh
I am renting a flat there in the meantime which is covered by my student loan
I want to buy a studio flat in marleybone at £175000
I have savings around £70000 for the deposit
I work part time for around £400 per month
I have private income of around £300 a month
If able to purchase the flat I would rent it out at £500 pw / £1800 p
QUESTIONS:
I’m not here to ask how much it’s going to be or how long it will take because there are online mortgage calculators for that.
I want to know if I will be ABLE to get a mortgage in my current situation?

No you won’t be able to get a mortgage. Why? You barely make anything. And it’s part time which means it’s shift hours and isn’t guaranteed and it’s not salaried which makes it difficult for anyone to guessimate how much you will make consistently as you might get fewer hours etc this week or that week. Private income can’t be registered as it’s done under the table or whatever, so there is no tax record of it.
How do you intend on saving up £70000 when you make only £400/month?
Unfortunately you won’t qualify for a mortgage at all.
No since you are buying it as an investment.
Your lack of income and full time employment are the problem.
Probably not, your income would not be enough to cover the mortgage payment, taxes, insurance, maintenance and upkeep and your regular living expenses like food, auto, insurance, university costs, etc.
Even if you were going to live in it, they wouldn’t give you a mortgage. Sorry, maybe at a later date you can work it out.