Sesh

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. 

Yes

Tax class 3 will be applicable for the whole year of 2018. File a tax return and claim back extra tax paid if any from January to August.  I hope the change of tax class was on 27.04.2018 and not in 2019.

Just a small correction.  Even though during mutterschutz full net salary will be given, a part of it is paid by health insurance. 13 euros per day. The rest is paid by the employer. Therefore it is necessary to give the certificate provided by the doctor to the insurance company,so that their part is paid at the right time.   Congratulations and all the best.