The Mayan language was both written and spoken. In the pre-Columbian era it was visually represented by Maya hieroglyphic script.
spoken language (the spoken form of a human language)
Usually, yes. But some languages do not have writing.
Corinthian German does not have an official written language, but steps are being made to write an official dictionary for the language.
Your primary language is the one most often spoken. Schools dealing with ESL populations and immigrant parents regularly query what is the primary language spoken in the home to help with home school...