Adjectives that come before the noun in German agree with the noun they describe based on gender, number, case and what article (if any) precedes it. So, if the noun is masculine singular and in the nominative case and is preceded by the indefinite article (ein), the adjective describing it must take a particular ending. It would take a different ending, for instance, if the noun were feminine or if it were preceded by the definite article.

A full explanation can be found here as it can be quite complex to begin with: https://en.wikipedia.org/wiki/German_declension#Adjectives. There are many other explanations available so do some research to find one that makes sense to you!

No. That would be : Es ist ein kleinerer Haushalt.

Ja--also because it is in the nominative.