Learn Russian: Иван выше мамы, но ниже папы. - Ivan is taller than mom, but shorter than dad.

In Russian, you can compare two things by putting the second thing in the Genitive case, completely skipping the word for 'than' (чем). Since Ivan is being compared to his mom and dad, мама becomes мамы and папа becomes папы.

Where do the words выше and ниже come from?

These are the comparative forms meaning 'taller' and 'shorter'. The adjective высокий (tall) changes irregularly to выше, and низкий (short or low) changes to ниже. They do not change endings to match gender or number, so you can use them exactly as they are!

Since dad is a man, shouldn't the Genitive form of папа end in -а or -я like other masculine nouns?

Even though папа refers to a male, the word itself ends in -а. Because of this ending, it follows the exact same grammatical rules as feminine words like мама. That is why its Genitive form is папы, perfectly matching мамы.

Could I use а instead of но for 'but' in this sentence?

It is better to use но here. The conjunction а is typically used when you are contrasting two completely different subjects (for example, 'Ivan is tall, but Anna is short'). Here, we are talking about the exact same subject (Ivan) and just adding a contrasting fact about him, so но is the natural choice.