# Is the grammar used in following sentence applicable to any similar situations?

This is my sentence:

How much a month is the rent for this house?

Similar situations

How much a two nights is the rent for this room?
How much an every two nights is the rent for this room?
How much an hour is the rent for this bicycle?

In your examples, only the last one works, because the other two have non-single nouns. This construction using "a" or "an" in place of "per" applies only to single-unit nouns, and is usually used to refer to an exchange of money.

This hamburger costs \$3.49 a pound.

My rent is \$250 a week.

My salary is 2000 bucks a month.

Bike rent is \$10 an hour? How much is it a day?

If you want to ask how much two nights would cost, you can ask,

How much a night is the rent for this room?

And then you multiply the answer by two. Alternatively,

How much is two nights' rent for this room?

That formulation with "a" (meaning "per") takes a time-noun in the singular: second, minute, hour, day, week, fortnight (British), month, year, decade, etc.

How much a month does it cost?

If you want to refer to an arbitrary period of time using a plural time noun:

How much does it cost every three days?

But there every doesn't mean per but refers to a recurrent event.