Do I have to pay tax if I spend all my income as a self-employed?

I’m participating in working on a project part time that will probably last for 3 months. I will get ~£7500 income for this. But at the same time I’m working full time in a permanent position. I wouldn’t like to get too much into being a business, so probably this will be my overall income as self employed.

This project has already started, so I’d need to join as soon as possible, and be able to sign the contract. I will also need to be able to issue invoices each month. Does it mean I need to register before I start any work? Also, which really confuses me is VAT. As I read, because of my low income as self employed, I won’t need to register for VAT. Does it mean in the invoice I won’t have to state VAT?

I will need some quite expensive equipment in order to perform better at this project, and I could spend all the income to that. If I do, I don’t have any earnings, so does it mean I won’t have to pay any tax? If yes, if I do this, I basically "run a business wrong". If for example in the future I want to open a company, and want to get loan, will the above action have consequences?