Learn Finnish: Pelkkä bensiini maksaa paljon. - The petrol alone costs a lot.

While vain is an invariable adverb meaning only, pelkkä is an adjective meaning mere or nothing but. Using pelkkä is a very natural way in Finnish to say just the item or the item alone. Because it is an adjective, it must match the case of the noun it describes.

Does the verb maksaa mean to pay or to cost?

It means both! The meaning depends entirely on the context and the subject. When a person is the subject, maksaa means to pay. When a thing or service is the subject, as is the case with bensiini (petrol) in this sentence, it means to cost.

Since petrol is an uncountable liquid, why is bensiini in the nominative case rather than the partitive bensiiniä?

Even though petrol is a mass noun, it acts as the definite subject of this sentence. When we talk about the item as a whole or as a specific defined concept (the petrol alone costs a lot), it takes the nominative case. You would use the partitive bensiiniä if the sentence had an indefinite quantity, like if you were saying you need to buy some petrol.

If I wanted to change this sentence to say the OTHER petrol costs a lot, should I use muu or toinen?

It depends on the context! You would use toinen (toinen bensiini maksaa paljon) if you are choosing between two specific types or options of petrol. You would use muu (muu bensiini maksaa paljon) to talk about the rest of the petrol in general, excluding the one you just mentioned.