"Mother tongue" and "native language" are the preferred terms. I've never heard anyone use "mother language." "First language" is also fine, but could also be used in a sentence about something other than your native tongue, in something like" the first language he learned was Spanish"

'Mother language' is not, as far as I know, a common phrase. I have never heard this used. I tend to use 'first language' and 'mother tongue' interchangeably, although language experts might claim that there is a difference. 'Native language' tends more to be used in phrases such as 'the native languages of the Amazonian rainforest', although it could also be used to refer to an individual's mother tongue.

We don't say "mother language" - that's mixing registers, and it sounds odd to native ears. The others are more or less the same.

National language