I was wondering, can you leave out the pronoun in a sentence if you have already conjugated the verb? (Like in Spanish). For example, does "Heb een hond" mean the same thing as "Ik heb een hond"? Would it sound weird?
No, but if you would drop the pronoun in Spanish, then in Dutch you can use the unmarked (unemphasized) form of the pronoun. Not all pronouns have such a form: there are "jij/je", "wij/we" and "zij/ze".
There's a detailed explanation here: https://www.duolingo.com/comment/3734337
As for the the pronoun 'ik', you can shorten that one to 'k. (And thus you only pronounce the 'k' part of 'ik'.)