S.B.
We own a rental property in North Richland Hills. Many of the things you are talking about are not required to be fixed by law. They are a nuisance and simply, not right in my opinion, but they do not affect your health or well being. Not being able to park in your garage is annoying, but not a hazard to your health or well being. At least according to the law.
Now the heater is a different story. With the affects of this ice storm, you need heat. He needs to fix it. He is responsible to make sure it is corrected.
You may also want to check with the city. I know in North Richland Hills, rental properties are required to get a certificate of occupancy. The city comes and inspects the property. They are looking for things to be up to code, but also checking to make sure that the property is being kept up (no large holes, etc.). Arlington is a much bigger city, so they may not require it, but if they do you may look into it and see if your landlord is going around things. I know in NRH, they do it through the water hook ups. New tenants can't get water turned on until the inspection is complete.
The dog has nothing to do with the landlord. Call the city and file something with code compliance about a barking dog. I know here in fort Worth you can file such complaints anonymously.
As far as what you can do. You could break the lease. But if the landlord chooses, he could sue you and probably win. You could owe all the money for the year and he could possibly keep your deposits. It's a gamble. He may decide that court is too much of a hassle and opt to just cut his losses.
You could contact the management and ask to be let out of your lease. They may willingly let you out of the lease, but most likely, they would expect rent from you until they get the house rented again.
I am sorry to say, but I am not certain you have any real course of action here (at least not one that may have serious repercussions for you). I would be sure to start documenting everything. Try to handle things via email or text, so there is a paper trail. Take pictures of EVERYTHING.
Be a thorn in their side. Either they will be annoyed and let you out of the lease just to be done with you or maybe, just maybe they will make repairs for you.
I would encourage you to make sure to not accept a property in such poor condition again. I realize it was a large deposit that was supposedly non refundable, but by moving in you accepted the conditions of the house. It's a shame your landlord is being unreasonable. And I don't understand how people like that can sleep at night.