Is the landlord or Tennant responsible for purchasing a air filter?

if you want an air purifier just like you want a portable heater or humidifier, you pay for it...

1. fix the leak

2. replace the moldy Sheetrock.

3. really how difficult is this?

Read your lease. I am sure the answer is in there somewhere.

The law does not get involved in people's personal business. It does not tell people how to run their business. What does the lease say? If the landlord does not state that he will do it, then, it is considered maintenance within the unit so it is the tenant's responsibility, just as all of the other maintenance within the unit, floor cleaning, vacuuming, etc. And, the air filter should be changed every month. You can buy cheap filters. You don't have to buy top of the line electrostatic ones.

maybe having a good cleaning of the house by professional people dealing with mold will do the trick

it would have to be proven that the odor is unhealthful to force the landlord to provide more than is included in the lease

Landlords have to provide a safe environment for their tenants, Mold could cause serious health concerns, You need MORE than an air purifier --- you have to professionally get rid of the mold,

Mold requires a source of water to live. So a roof or pipe leak or a AC condensate leak or something else is supplying the water. If that is fixed the mold will die off. It would still need some treatment but that would be a big step. A filter would not help at all.

The tenant pays for the air filters.

Mom NEEDS to get seriously educated about Reality of tenants LAWS in TX.

She NEEDS to replace air filter Quarterly.

As for MOLD , she will be paying for certified licensed inspection.

IF NOT , she will be legally Liable.

1st of all, that mold needs to be inspected by a qualified person - it could be worse than anyone knows; 2nd - a purifier will not help w/a mold issue............and Mom would do good to look online at the tenant/landlord laws for TX - it will be beneficial for her + tenants