edit: I should be less eager to click buttons

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Where do I begin…

'spelling of conscientious'

This would be covered in the first editing pass when I turn the spell checker on. I don't see what this is meant to demonstrate. Even good writers have trouble remembering how some words are spelled.

'explain oxford comma'

What's the point of this?

'repeating a tongue twister; I like the “Betty Botter bought a bit of butter” one.'

What's the point of this?

'Questions about rules in ‘Elements of Style‘'

Elements of Style is not a rulebook. It's a stylebook.

'A few puzzles to test their creativity.'

A good writer is like a good designer. You either like their style or you don't. If you don't, you'd never ask them in for the interview. A quick writing sample is the only test of creativity you need.

'More spellings and grammar questions.'

A writing sample is all you need to assess grammar and spelling competence. My grammers is fine, but I couldn't recite rules and practices in a test.

'Some domain related question, for e.g. ask sports writer, the dates when the last football world cup was played.'

A good writer knows how to research. If you need an x writer for some cultural reason then you'd ask for that in the ad. This is a poor filter since it doesn't tell you how well a writer can write on the subject.

'Question on lexical roots of some words.'

Is this an English class or an interview?

I would show myself the door pretty quickly and advise all my writer friends not to consider your company. Your interview questions display a serious ignorance of the craft of writing. Save yourself some headaches and ask the best writer in your office to hire other writers. The sort questions you ask are easily rehearsed by a bad writer with good memory.