Dear Rabbi, I have heard from some who say, one should not read Tanach at night which inclouds Tehilim. On the other hand, I have heard that David hamelech mentioned saying Tehilim is not only praying but also counts as learning. I am confused if reading tehilim after chatzot is allowed/ suggested. Ty for your time.

There are several sources which say that it is better at night to learn the Oral Law, rather than the Written Law. It's important to know the secondary or tertiary halachic clout of these sources which just want to stress the preference of the Oral Law at night. But if one is not studying Talmud, saying Tehilim or learning the Written Law is clearly not only prohibited but it's the best thing in the world one can do!! Saying Tehilim is even less "problematic" than other Written Law even for these few sources, for as you wrote, it's like prayer and not really learning. How much more so, regarding the chapters of Tehilim which are customary to say precisely at Chatzot, middle of the night!