I am a language student in Germany. my visa has expired a month ago and i have applied for an appointment for visa renewal and got the appointment for 4th February 2019.But due to a personal issue i am discontinuing my study in Germany. so can i travel back to my home country India immediately without renewing the visa on 4th february 2019. without any special papers or documents, that is, with only my passport? if i need any documents where? how? should i get it?
Overstaying your visa is illegal in Germany. The Act on the Residence, Economic Activity and Integration of Foreigners in the Federal Territory provides an English translation of the consequences of overstay. It very much depends on whom you will meet in this process. My best guess is that both renewal and travelling out of Germany will be an issue at the moment.
Travelling out of Germany without getting your visa fixed wouldn't be my advise. My advise would be to ask for help at the 'Ausländerbehörde' and be as polite as possible. If you leave the country without doing so, you would face a fine and you would not be allowed to re-enter. Your best bet is to renew the visa first, you'll probably have some stern words of the officer involved but at least you have the possibility to return and you might not have to pay the fine.
If you applied for your visa renewal before your old visa expired, you should have received a "Fiktionsbescheinigung" (§81 Abs 4 AufenthG, https://dejure.org/gesetze/AufenthG/81.html). This document is usually as good (edit: for travelling between Germany and your home country) as the visa you had before.
At least this is how it works for people who have a visa for attending a regular university. For language courses at private language schools it may or may not be somewhat different.