I am not a lawyer. I have been a multifamily landlord for the last 4 years and negotiated commercial leases before that. Before I go on, without seeing the specific lease, everything below is just what a lease will normally say.
1. Most leases and contracts will spell out where any legal actions have to take place. You will typically find it in the last 1/3 of the lease somewhere.
2. It is not illegal in Texas to withhold late fees from the security deposit. Unless the lease specifically says you can't and assuming the late fees are not unreasonable, you should be OK.
3. You likely could sue them for late fees if you determine you can't withhold from security deposit but I'm not sure it would be worth it. Legal fees would probably cost more than the late fees amount to. Most leases do not require demand for late fees. In the Texas Association of Realtors (TAR) promulgated lease, it says "If Landlord does not actually receive a rent payment in the full amount at the designated place of payment by the _______ day of each month at 11:59pm, Tenant will pay Landlord for each late payment...." Notice it says "Tenant WILL pay". It says nothing of Landlord having to make request for said late payment. The Texas Apartment Association (TAA) lease is similar. It says "If you don't pay all rent on or before the ________ day of the month, you'll pay an initial late charge of ____". Further, both of those leases explicitly state that the Landlord can deduct late charges from the security deposit.
I feel confident in saying that if you used either of these lease forms, you are in the right unless your late fees are deemed unreasonable. "Unreasonable" is a legal term but as long as you can show they are not out of the ordinary, again, you will be fine.
You can read the Texas Property Code relating to late fees here: http://www.statutes.legis.state.tx.us/Docs/PR/htm/...
You can read the Texas Property Code relating to security deposits at the link below. This encompasses several sections but starts here: http://www.statutes.legis.state.tx.us/Docs/PR/htm/...