I'd like to know if there are languages where there aren't words for father and mother, but for parent, and how one would say [something like] this to their father in that language: where's mom?
I think it could be: where is parent?
It also could be: where is the other parent? [strange]
Or...
Where is the female parent? [sounds unnatural, maybe it's not in a language other than english]
The only such language I know about is Pirahã, the indigenous language of the isolated Pirahã people of Amazonas, Brazil. It is minimalistic in many ways, having the least number of phonemes (only 11), lacking words for numbers and for colors. Daniel Everett, the greatest specialist on Pirahã who spent years living with the tribe, states Pirahã has the same word for mother and father:
Everett (2005) says that the Pirahã culture has the simplest known kinship system of any human culture. A single word, baíxi (pronounced [màíʔì]), is used for both mother and father (like English "parent" although Pirahã has no gendered alternative), and they appear not to keep track of relationships any more distant than biological siblings.
To approach this from a different angle, I am married to a Xhosa woman. There may be no word in her language for 'parent' in the sense of a biological parent. Rather, mothers and fathers are those who belong to the next generation up, in other words one's biological parents and all of their siblings. Sometimes the siblings may be called tata mncimnci (small father) or mama mncimnci (small mother), or tamnci and mamnci for short.
The Afrikaans language has absorbed this in small corners of the language (they are rare words in Afrikaans) as kleinpa and kleinma. Those are the finer details, sometimes encountered. But in practice, 'mother' and 'father' refers to a group of people one generation up. In a sense, then, there may be no words for father and mother as we know them.
Another such language, though fictional, is Mando'a. Mando'a is spoken by the Mandalorian faction in Star Wars. As stated by the creator of the language, Karen Traviss, Mando'a is regularly gender-neutral.
Gender nouns are the same for men and women. Gender is implied contextually, if relevant. Where gender clarity is necessary, the adjectives jagyc (male) or dalyc (female) are added.
The word for parent is buir, and it is used regardless of whether or not the parent is a birth parent or an adoptive parent. Family is highly regarded in Mandalorian culture, but in a manner that is very much different than the Pirahã in @Yellow Sky's answer. There is very little emphasis on adoption versus birth, and families (known as aliite, aliit singular) are made up of larger organizational units comprised of those related by blood, family friends, and pets. They are also lead by a clan buir who is responsible for leading and representing the clan.
When addressing a parent, "buir" is often used as a suffix, much like Japanese Honorifics. Kal Skirata, the Mandalorian training sergeant responsible for training Omega squad, is called Kal'Buir by the clones he trained. This is because of the relationship they shared on Kamino, but also because he later adopted the members of Omega squad as his children.
To address the specific questions at the end of the post, "buir" can be treated very much like the Japanese honorific Sensei. When addressing a teacher or speaking of them, they can either be addressed as "Sensei", context permitting, or addressed as their name followed by "-Sensei", such as "Akari-Sensei".
Also, it is important to note that this post draws heavily upon Star Wars Legends, but that's a topic for another SE.
I can only post two links, otherwise I'd post more sources for my post, but some reading points are the Mando'a Legends page on Wookiepedia and The Mandalorians: People and Culture by Karen Traviss as printed in Star Wars Insider 86.
