If you're smart you'll keep it concealed from casual observation to prevent being unnecessarily hassled.
TX Penal Code makes no differentiation between loaded and unloaded guns. If it's legal to have a gun in a particular situation, then it's legal for it to be loaded.
Posession means that it's easily accessible to passengers/driver. Since the law relates to posession you can have it anywhere you want. The law does not allow you to carry it on your person once you leave your vehicle .
The new law basically gives you the benefit of the doubt if you're caught with a handgun in your vehicle. It says that the LEO is to presume you're travelling if you're caught with a handgun in your car. TX law already allowed a person to carry a handgun in the car while travelling.
IF for some reason the LEO feels that he has decent evidence that you are NOT travelling, and the DA decides to prosecute and can prove that you were not travelling then you're going to be penalized.
The old law put the burden of proof on you to show that you were travelling, the new law puts the burden of proof on the government to show that you weren't. There still is not a good legal definition of what travelling is.
If you DON'T have a CHL, you are not required to tell an LEO that you are armed. If you are smart and have the gun concealed then it should be a non-issue. Remember that anytime you are stopped, you will be asked for proof of insurance--if you keep it in your glove box like I do, it's not smart to put your gun in there with it...