Can you start a question using 'Meanwhile'?

Meanwhile may be used to start a sentence, but not in the way you have attempted.

“I was absent with illness. Meanwhile, my colleagues dealt with my emails”. Meanwhile here refers to the period during which I was ill.

Meanwhile =

until something expected happens, or while something else is happening:

Cambridge dictionary

Meanwhile has the connotation that something else is, was, or will be happening; during does not.

You have used the word as if it were synonymous with during; this is incorrect usage.

During =

at some time between the beginning and the end of a period:

Cambridge dictionary

Meanwhile is an adverb. Like all adverbs it can start a sentence:

Meanwhile, comma in my absence, did you receive an answer to your mail by one of my colleagues?

Recently, comma in my absence,

On Tuesday, comma in my absence,

etc.

OED: B. adv.

1. During the time intervening between one particular period or event and another; while or until a particular event occurs; at the same time; for the present.

1877 J. A. Froude Short Stud. (1883) IV. i. x. 113 The archbishop meanwhile had returned from his adventurous expedition.