I often hear "papa" and "mama" in animes, in situations where they seem to mean father and mother. is that so? are these words borrowed from the spanish words "papá" and "mamá", which mean father and mother? Which kanjis do they use since father for example is also お父さん and I dont think they use the same kanjis, do they?
mama = ママ papa = パパ are relatively recent borrowings, always written in kana,(usually katakana) that exist beside the native terms 母 (haha) and 父 (chichi). In old Japanese, the word for mother 母 would have be pronounced in a way that sounded more like "papa" (as a bilabial fricative). There are also the native honorific readings (okaasama, otousama). And WWWJDIC lists multiple other readings of the same kanji, either childish (kaka, and toto) or outdated, as well as the on-yomi (bo and fu).
In anime, ママ パパ, are informal, don't combine with honorifics. Children use them freely. Older Teenagers and adults are less likely, but it depends on the particular family dynamic. In adult company, you would be wise not use "mama" to speak of your own parent (use haha) or someone else's (use okaasan).
It's not clear from which language the words パパ and ママ were borrowed. English, Portuguese, Dutch and several other European languages use mama and papa (or close variants). Any or all may have influenced Japanese.
Papa and Mama is intertional word , it's came from baby saying Pa amd Ma ,a lot of European language use it ,also asia and many country, so Japanese may be didnt borow it from other but if think about what language influence this word to japan I think it is Chinese language btw I have heard chinese people also call their parent as Papa and Mama too event they already has another word too call their parent like japanese. In Teochew chinese (not main dialect which known as Mandarin chiness) I heard they call father as Pae (vowel short and ae sound more like e in word "Bed" and word "letter") and call mother Ma ( Hightone) i cant remember in mandarin and canton chinese In japane their is Haha and Chichi as mom and dad for casual word but it seem they also call their parent papa mama (not in just anime) for vey casual and have word Okasan and Otosan for formal and very respective.