Texas Apartment Monthly Pet Fee?

Pet rent is perfectly legal in most states. There is also no limit in most states. This is an international site so you will have to look up the laws for TX to be sure.  Tenants should always find & learn the laws for your state anyway. You cannot protect your rights if you do not know what they are. 

It's legal but most charge just a one time fee and possibly raise your security deposit.

Yes,it's legal, so, yes, they can charge the fee.

If you don't like it, move when your lease it up.

Not illgal, but a rip-off.

Should be in your contract.  Dogs are allowed, what weight and breed and cost per month. 

I have never known a pet fee to be that high on apartment of that rent.

My daughter is looking at luxury apartments in downtown Indy. Rent starts at about $1300+.  $250 one time pet fee plus $25 per month per pet. 2 pet max

It is legal, just as it is legal for you to choose not to live there and to find a place that has terms you find more favorable.

Yes they can.

Your options are to pay it; or to find somewhere else to live with your pet. 

Yes.  If that is what you agreed to in the lease.

If that is one of the terms/conditions of living in the place with a dog then yes you accepted those when you moved in and/or signed a contract