As someone with self-employment income, you will be sent a self-assessment tax return in April every year, on which to report your total income (both employed and self-employed) for the tax year that has just finished.
Your PAYE tax code will not need to change, unless, when you are completing your tax return, you ask for the tax on your self-employed work to be collected through your wages in the following tax year. If your combined income goes over £40,000 in the tax year, the amount of Class 4 NI payable starts to be restricted (more details).
This is completely optional, so your tax code does not need to change if you do not want it to.
However, if expect your self-employed income to be less than £5,885 per year, you will can apply for an exemption.
Generally, expenses are allowed if they are incurred for business purposes.
I don’t understand though in my PAYE employment; my tax code has suddenly changed from 547L to 747L.