Hello @Sherwin15
Welcome to the Wefugees community and thank you for your question.
Yes, you can apply for asylum if you are residing here with a student visa. Your family can do so as well, but only if they are in Germany (it's not possible to apply from outside, e.g. in an embassy). If they are still in your home country, you can let them come to Germany through family reunification after you've been officially acknowledged.
Best regards,
Thorgen