For one, the startup doesn't exist yet, so until March I will get nothing on hand, though I have enough reserves to bridge that time.
I would not take this deal unless the start-up exists in some form. If it's just not yet profitable, then there's a risk/reward to consider. If it doesn't exist at all, then it cannot make a legal obligation to you and it's not worth taking the deal yet. If everything else is an acceptable risk to you, then you should be asking the other party to create the company and formalize the agreement with you.
As regards reserves, if you're really getting paid in shares instead of cash, then you may need them later. Shares in a start-up likely are not easy to sell (if you're allowed to sell them at all), so it may be a while before a paycheck given what you've described.
For a second, who pays the tax? This is my first non-university job so I don't exactly know, but usually the employer has to/does pay my taxes and some other stuff from my brutto-income (that's what I understood). If brutto=netto, where is the tax?
This I cannot answer for Germany. In the U.S. it would depend in part on how the company is organized. It's likely that some or all of the tax will be deferred until you monetize your shares, but you should get some professional advice on that before you move forward. As an example, it's likely that you'd get taxed (in part or in whole) on what we'd call capital gains (maybe Abgeltungsteuer in German?) that would only be assessed when you sell the shares.
For third, shares are a risk. If I or any other in the startup screw really, my pay might be a lot less than expected. Of course, if it works out I'm rich(er).
This is the inherent risk of a start-up, so there's no getting around the fact that there's a chance that the business may fail and your shares become worthless. Up to you if you think the risk is acceptable. Where you can mitigate risk is in ensuring that there's a well-written and enforceable set of documents that define what rights go with the shares, who controls the company, how profits will be distributed, etc. Don't do this by spoken agreement only. Get it all written down, and then get it checked by a lawyer representing your interests.