Will a refused Schengen entry affect application for a UK EEA family permit?

If your relationship and travel plans qualify you for free movement under European law, you can only be denied an EEA family permit on grounds of public security, public health, or public policy. An adverse immigration history is, in itself, not a sufficient basis to refuse the EEA family permit.

As implied in a comment, however, if the reason for cancellation of your Schengen visa points to issues of public security, public health, or public policy, those issues could independently lead to a refusal of the EEA family permit. These grounds are fairly serious, and most people will not be affected by them.

In fact, the UK should not even be asking about it. But they do, and because they are planning to leave the European Union, you should fill the form out completely and honestly. If you do not, your answers on that form could be taken as deception, which would make it difficult for you to enter the UK without your husband or after the UK leaves the EU.

What should I call it: deportation or refused entry?

Refused entry.

Should I should mention it while filling in the online visa application form?

Yes, you should mention it (see above) because failure to do so could make it difficult for you to enter the UK outside of the free movement rules.

Can it affect the issuance of the visa?

It should not, but it is possible that it will. In addition to the considerations mentioned above, it could simply increase the chance of an improper refusal.

In the application form, I can't find a place where they specifically asked "refused entry from any other country". Should I give every details of what happened on the additional information?

Just answer every question completely and honestly. If they do not ask about entry refusals, do not report the entry refusal. If they ask about having a visa cancelled, say that your visa was cancelled at the German border and explain why.