I would like to ask you a new question: I am a PhD student employed by the German University(Under 4 year contract). I am currently insurred by TK. Can I change this insurance agent and apply for an insurance in a private company like Mawista? What happen with social insurance if I change the insurance company? Now, my social and health insurances are paid through TK

you can change your health insurance if you are registered with them for more than 2 years ( or 1.5 years).
You do not need to think about other things. those will work automatically.

if you are 30 years young student you have to be insured by Gesetzliche (national) agencies (am not sure). Secondly, if you are a BATx/2 (civil servant) you probably do not earn enough (ca less than €2.5-3.3K pm) to be exempted Gesetzliche agencies. Am not sure if after your 30th birthday you can switch to private KV despite earning little, but you can only switch to another Gesetzliche after 18months (they have to give you a kind of recomendation)

Social insurance is not affected I guess