For a long time, «мили́ция» had been the word for Russian police. Then, during the 2009-2011 reform the name was changed to «поли́ция». The «милиционе́р» then becomes «полице́йский»
Still, expect native speakers to use мили́ция and милиционе́р in speech for quite a while.
"Election(s)" is always plural in Russian.
Russian has a formal verb «являться» which means "to be". The verb is reflexive. Its use is characteristic of formal writing and not necessary even there.
However, there are some contexts where it is hard to do without it. For example, if you have a subordinate clause or a verb phrase where "to be" is the main verb (omitting it does not work well in this case):
Or, well, you can use a participle if you are that formal. Here, you can also use a Dative impersonal construction, which means about the same (eg. «Ты никогда не смо́жешь поня́ть»→«Тебе́ никогда не поня́ть»):
You can use either «премье́р-мини́стр» or a more colloquial word «премье́р» (which is behaves as a typical masculine noun)
Officially, Russia has no position under the name of "prime minister", however, the Chairman of the Government is commonly called a prime minister in speech and in media. Which is why we teach it.