Why can't you say tehillim and learn Tanach between shkia and chatzot (midnight)

who told you this?

The Tzitz Eliezer has a T’shuvah on this and brings down several different opinions about what is a problem and when. There are several Minhagim by this and certainly not everyone is Makpid. There are those (including the T”E) who hold that Tehillim is always okay while he also brings downs opinions, if I recall correctly, that Tehillim was Davka the problem.

Some people refrain from reciting tehillim after sunset till chatzot because those are the hours that “midat hadin” operates and tehillim is “midat harachamim”

However, there is no halachic basis for this minhag.

I’m not sure that it’s an issue of “learning Tanach”, meaning something like taking a shiur on the parsha or the like. I think the issue is with something like pamayim mikra v’pam targum. My husband does his during daylight hours, but he says that it’s OK on Friday night. Not sure what the svara is.

Sam2, that is actually what I meant – pamayim mikra is simply saying the pseukim, not learning meforshim, so this would be problematic, but going to a chumash shiur at night would not, are we saying the same thing?

I’ve never heard of this. However, whether to learn on Nital Nacht (Xmas eve according to the most well known opinion) sounds a bit similar. When a group of us asked our Rov his position, he said, “You should know that there a several different shitas as to what the actual date of Nital Nacht is. So some people are very machmir to fulfill all opinions and don’t learn for the entire winter.” So my position, backed by my Rov is to learn at will what I want whenever I want unless barred from doing so by actual halacha (such as Gemara on Tisha b’Av).