When I was studying Russian in the 1970's, I don't recall "shavovat'"--it must not have been considered standard at the time. However, "telefonirovat'" (to phone) was gaining acceptance.
Verbs so constructed invariably follow the ordinary conjugation of any native Russian ''-ivat' '' or ''-ovat' '' verb, e.g. just as razgovarivat', to converse, to chat.
Because such a word does not exist. Russian uses many words borrowed from German, French and English, but the borrowing occurs when there is no native word. For example, the word "horizon" is written (and spoken) as "gorizont". There was an unsuccessful attempt to create a native word, but it was beyond laughable.
However, "telefonirovat'" (to phone) was gaining acceptance.
Only in exceptionally formal speech. I think it was used in translation of Hercule Poirot stories. Also, the word "telefonogramma" meant a phone message received and recorded on paper. It's largely obsolete and will cause strange looks if used, just as if in English you refer to someone's car as "jalopy" :-)