Do you pay rent to your common law spouse?

It could be her share of the mortgage. Though I don't why she would call it rent. But I know couples who go in half on the bills. Then there are those couples who just get the bills paid and split or come to an agreement on how to spend the rest or decide where it should go.

Is it some tax/benefits scam?????

Sharing responsibility is normal but why phrase it as paying rent. That sounds odd. She is sharing responsibility.
If they intend to be together long term she should consider having a legal vested intrest in the property but again some people are content to just allow their partner to own certain things.
I own a property that my husband dosen't but we are married so in the event of a divorce he would definitely be inclined to get half.

An owner of a resident can charge rent or not charge rent to people living there.

If she was on the Title she would be paying part of the mortgage so rent makes sense to share expenses

Mostly I have seen this (married or common-law) when both work and the mortgage or payment/rent is proportional, adjusted based on their income.

If two are married and have a joint account, the result is about the same.

I know a couple who live together but for Universal Credits (Social Security Houseing benifits) reasons she is renting from him they are paying the Mortgage like this

That’s weird 👀

That seems unusual in marriage...

She is a foolish lady

My state doesn’t have "common law" marriages. So if they lived here and didn’t co-own the home, she’d legally only be a tenant.

Nothing normal about it.

How much does she pay

If they broke up she would have claim to the house in the province I live in.