Learn English – “BY” as an Adverb

"Mind" is followed by an "-ing" form when it is followed by a verb. This is a strict rule. So we must proceed like this:

Would you mind having...?

"Explain" works like this: explain something to somebody.

Can you explain the rules to me?

Now we have to combine the two rules, remembering "mind" needs a verb in present participle, and "explain" needs "to + person":

Would you mind explaining to me why you didn't show up last night?

Is the winner. The way we link verbs to other verbs, or use them with objects is commonly called Verb Patterns). Take a look at the basic article linked before which summarises the different types.

Scissors is plural, like trousers, and that must be followed by a singular. The sentence can be made grammatically correct in two ways: by adding pair of (because a pair is singular), or by replacing that by its plural, those.

Please pass me that pair of scissors
Please pass me those scissors

These are both grammatically correct but, as this Ngram shows, the second version is a lot more common.