"My mom likes cooking."
Translation:Моя мама любит готовить.
When using "нравиться," the person that likes the thing or activity goes into the dative case. So, "Моей маме нравится готовить" would work here.
"Готовить" is a verb in imperfective aspect (process) while "приготовить" is in perfective aspect (result).
The imperfective is used for the present (it is in progress).
The perfective can only be used for past or future (the result can either be reached in past or in future).
I would say that "готовить (еду/пищу)" is a very broad term and it includes "варить", "жарить", "тушить" or maybe just "резать" in case of a salad consisting of raw vegetables. So speaking about the Russian sentence above I don't think that "варить" is an exact substitute for "готовить". It can be if she happens to like exactly that, but maybe she only likes "жарить".
Hm, a quote from wiki: "Food preparation includes but is not limited to cooking".
EDIT: The Cambridge Dictionary defines cooking as "the activity of preparing or cooking food". The best translation for this kind of activity in Russian is "готовить".