The phrase "and question how" is correct and usable in written English.
It can be used when discussing the act of questioning or examining the manner in which something occurs or is done.
Example: "We need to analyze the results and question how these changes impacted our overall performance."
Alternatives: "and inquire about" or "and examine how".
Then I'll go home and question how much I like or need it.
"But I do go out every time and question how we make photographs of the world.
"Maybe I'll bring to attention the words that were used and question how hurtful they were," Ms. O'Shea said, "and the other person will say, 'I don't think it was wrong' " to say that.
As Tyler described his conception, production, and design choices, it was clear they were meant to poke holes in ideas of ownership and identity, and question how our style choices articulate stances in these arenas.
Others are more sceptical and question how auto-enrolment will relate to state benefits and whether lower-earning employees will be able to afford their contributions in these straitened times.
He and other Democrats portray his opponent as out of his league in Washington and question how much he knew about a political scandal that sent a local Republican chairman to prison.
Notes and questions How has Paul Ballard got the money to hire a doll?
Some readers thought your profit margin was too low and questioned how well your business was doing.
Another Iraqi official said that Trump's suggestion amounted to "looting," and questioned how the new Administration might do it.
In shaky English, the woman expressed reluctance, and questioned how she could be sure he would keep his word.
Some analysts had criticized UBS for lacking a clear strategy for the investment banking unit and questioned how big the business should be within UBS.
