Sesh

You cannot get an Indian passport being a German citizen.  For this you need a letter from amt stating he/she is not a German citizen which they will not give as they say it is for the child to decide when he / she is 18 years. Therefore for the moment the child will be a German citizen and will need to get German passport and on turning 18 they can decide for themselves.  A work around if you really want Indian passport, is to have birth in India. In that case the child will get Indian citizenship and passport before 18 years. 

It is covered. Because elterzeit and Elterngeld time starts on the day of birth of child.  So after 8 weeks of mutterschutz are done, Elterngeld will take over. In the case GMan mentioned between June 29 and July 4, Elterngeld will be paid pro rata basis. Whatever is the amount for a month will be divided by 30 and multiplied by 5. 

The elster software is simply a copy of paper forms. So filling it up is pretty straight forward.

Paper forms I am not sure of. Sorry

You should have received 2 lohnsteuerbescheinigung. Fill as it is mentioned on them. Tax class for each of them will be mentioned on them. You can add extra lohnsteuerbescheinigung in elster after the first one.  For arbeitlosengeld in Hauptvordruck it's on page 3 or 4 under Sozialleistungen I guess. Select arbeitlosengeld from drop down and fill the amount  you received.  For all the three items you need to mention their period.