I went to the Gewerbeschein office and they said that a freelance English Teacher doesn't require this special permit. I visited the tax office to ask about invoicing and they said simply to note your tax number on the invoice and that it's better
not to charge MwSt because you get taxed on that even though you hand it over to them.
The way the tax office explained it to me was: say you invoice 100€ and tax of 17€ (for example), total 117€. You have to pay income tax on 117€
AND give that 17€ directly to the tax office.
So you are taxed on money you don't even get to keep!
Some companies insist that your invoice show tax on it - it doesn't have to (said the tax office) but to appease your customer you can simply reflect the additional tax burden in your fee. Companies can never explain why they believe YOU need to show tax on your invoice... and it's because you don't need to.
Regarding deductions... there's more to it than the average tax consultant is prepared for so find one that you are convinced knows what you need. I learned this after some years here. There is a special section for Teachers (just like with the Gewerbeschein) and the other for freelancers and with the right tax consultant you can deduct your computer and pretty much anything and everything work related - as it should be. However, it could depend on your employment "status", which is fairly easy to have altered, within reason, for tax reasons. My immigration office balked at the idea of altering it at first but after a nice letter explaining it from my tax consultant, they changed it right then and there.
And yeah, my tax consultant is a former student. It's a good way to get tax assistance and earn money!