Swiss Code of Obligations OR Art. 323b requires that the employer give the employee a written pay slip:

"Article 323b
3. Wage security
1. The employee shall be paid in money in the legal currency within the working hours, unless otherwise agreed or customary; the employee shall be provided with a written statement of account."

https://gesetzestexte.help.ch/or/art...Arbeitsvertrag

Since your employer is not doing this, it might be advisable to obtain legal input on next steps. The City of Zurich provides limited free legal advice by telephone as described at this link (German):

https://www.stadt-zuerich.ch/portal/...sauskunft.html

For missing AHV payments, you will need to prove to the Compensation Office (Ausgleichskasse) that you were employed and that the deducted AHV social charges were not transferred by the employer to the Compensation Office. A pay slip would demonstrate this:

"33. What happens if your employer does not pay the contributions?

If your employer has not fulfilled his legal obligations and has not paid the contributions, there is no disadvantage for you if you can prove the deduction of contributions in a proper way. The income you earned will still be entered in your individual account. The best way to prove this is with pay slips, from which the deductions can be seen. If you cannot provide proof that your employer has actually deducted the contributions from your salary, the Compensation Office cannot register the corresponding income.

https://www.bsv.admin.ch/bsv/de/home...herte/ahv.html

Good luck!