Learn Croatian: Ima puno udubljenja po haubi. - There are a lot of dents all over the hood.

While ima literally means 'has', it is frequently used as an impersonal verb to mean 'there is' or 'there are'. In Croatian, this impersonal ima never changes its form to match the plural items that follow it. You could use postoje (there exist), but ima is the most natural choice for everyday speech.

What case is udubljenja, and why does it look like the plural subject form?

It is in the genitive plural. The word puno (a lot of) expresses a quantity, which requires the noun that follows to be in the genitive case. For the neuter noun udubljenje (dent), the genitive plural is udubljenja. It happens to be spelled exactly the same as the nominative plural, though in spoken Croatian, the final 'a' is drawn out longer.

How does using po haubi change the meaning compared to na haubi?

If you said na haubi, it would simply mean the dents are located 'on the hood'. Using the preposition po with the locative case adds a distributive sense, meaning the dents are scattered 'all over' or 'across' the surface of the hood.

What is the base form of haubi, and is it standard Croatian?

The base form is hauba (car hood). It is in the locative case here because it follows the preposition po. It is a very common loanword from the German 'Haube', heavily used in everyday speech, though the strict standard Croatian term is poklopac motora.