Concerning your 1.) question:
I found two leaflets about how to proceed after receiving Subsidiären Schutz. They both advise that you get in contact with a lawyer that is specialized on asylum and/or migration law.
The obvious problem is that lawyers are expensive - but at least the state will compensate the costs in case you win and you can apply for "Prozesskostenhilfe" (legal aid) beforehand when making an appeal. In addition your lawyer can apply for financial support by the association "Pro Asyl". That is helpful since it is common to pay a certain amount of attorney's fees in advance which can be a challenge for refugees with a limited budget.
Still it seems to be a good idea to appeal. Especially because the decisions by BAMF seem to be arbitrary. For example Syrians get Subsidiärer Schutz since March 2016 way more often than before, even though the situation in Syria did not get better at all. Still they would have to fear persecution and a life-threatening situation if they would go back. Therefore they technically have a right to get a refugee status.
Plus: people with Subsidiärem Schutz can not make demands on family reunion until March 2018. So if your partner has relatives in his home country that he wants to bring to Germany (and that fall under the regulations of people entitled to take part in family reunification process) it is a good idea to appeal.
Sources (both German language):
Here is the results of my research concerning your 4.) question:
After the Subsidiärer Schutz is over (after 1 year) it can be extended for another 2 years. Your partner has to apply for this extension while the 1-year period of validity of his Subsidiärer Schutz is still ongoing.
After applying the Ausländerbehörde (aliens department) will check if the situation in his home country changed for the better or if there is still reasons to provide him with shelter. If they come to the conclusion that the situation got better then the BAMF will further investigate if the circumstances changed drastically enough to deny an extension of Subsidiärer Schutz.
Keep in mind to apply for the extension at an early stage because then he will be treated as someone who still has a valid residence permit until the decision of Ausländerbehörde. Even if it's already past the original expiration date.
Source (German language): https://www.nds-fluerat.org/leitfaden/10a-fluechtlinge-mit-aufenthaltserlaubnis-nach-25-abs-2-satz-1-alternative-2-aufenthg-subsidiaer-schutzberechtigte/10a-1-aufenthaltsrechtliche-situation/
I hope this helped to clarify the situation. If anything remained unclear, feel free to ask.