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My name isXXXXX a licensed attorney (State Bar of Texas).
Glad to try and help out. I'm pleased to share the following information.
Here's how this works. No, the conduct you mentioned (none of it) is unlawful per se. Texas has no statute addressing leaving animals (dogs or otherwise) in a vehicle, period. None. This is unlike a number of other jurisdictions, but it's true. What we do have, however, is a general "animal cruelty" law. If you want to see how that works, here's the best source to check out:
Lopez v. State, 720 S.W.2d 201 (Tex. App. 1986)
If you have a follow-up question or need clarification, please just say the word by using "reply" to reach me.
I truly hope all works out for you.
Thanks for your helpful information. I have no additional questions at present.