Merriam-Webster's 5th definition of battery, specifically relating to "a battery of"
a (1): a number of similar articles, items, or devices arranged,
connected, or used together
Examples: They ran him through a battery of tests. They offered a battery of filing cabinets.
b: a usually impressive
or imposing group, array
Example: After finishing my drawing, it was shown to a battery of specialists.
Dictionary.com's 2nd 4th and definitions
2: any large group or series of related things
4: a group or series of similar articles, machines, parts, etc.
Battery comes from a Middle French word meaning bombardment or assault. This is most likely why the word is most often used with "battery of questions" or "battery of tests" to imply that one has been bombarded with many questions or tests. In addition, in modern English we still use battery in the context of "assault and battery." And "to batter" means to "beat with successive blows."
So while "a battery of" can be used to talk about a group of similar things, the word also has a strong connotation of assault. And that should be considered when using it.
For your provided example sentences, all of them are correct. I would suggest that they also imply a rigorous process because of the use of "battery." But I think that is in line with what the sentences are trying to convey.