I've actually decided to keep it outside, so on that note, should it be okay?

Don't know enough about your microclimate (except that it's Texas vs e.g. England, a more appropriate climate), or conditions you'll keep it in. Don't grow it in tropical conditions because it's not a tropical, a garden plant or a house plant.

Well it'll be kept mainly in shade with the exception of maybe 3 to 4 hours of direct Sun, in the summer it can reach 100 so then I'll move it more into the shaded area! Other than that, should it be okay? Anything to watch out for?

The leaves are starting to look like this? What does this mean?

Either too much water or too much heat.

I can't answer for

Okay so don't move it around? and keeping it inside Under two t5 fluorescent lights will be okay? I'm just trying really hard not to screw this up! and the fluorescent don't give off too much heat so its probably over-watering, yet i noticed around the edges of the leaves were browning, could that be from when I put it outside in the sun? what would be the ideal conditions for a Chinese elm, thats all i have to know.