In these sentences, "has" should be replaced with "have" for both statements.

"My mother and father have a big bedroom."

"My brother has a bike."

As for using "was" or "were", "was" is used when referring to singular subjects in the past tense, and "were" is used for plural subjects in the past tense.

For example:

"He was at the store." (singular subject)"They were at the park." (plural subject)