"The bottle is full of beer."
Translation:הבקבוק מלא בבירה.
It's a risky business, trying to translate prepositions word-by-word. Instead, think of the definition of a verb as including which prepositions go with it, and it is more or less arbitrary, although there are patterns. מילאתי את הבקבוק בבירה, הבקבוק מלא בבירה, because the verb למלא - to fill - takes a direct object which is the container, and an indirect object with a ב which is the content.
A bit more information about this, the verb does have another option where both the container and the content are without a preposition. מילאתי את הבקבוק בירה, הבקבוק מלא בירה, that is also correct. But של is nowhere on the definition of מלא.
Is the word מלא in this sentence the past passive form of the verb "to fill" and pronounced as mil'e? And the מלא used as an attribute (m.s.) is pronounced mal'e. Is that correct?
I hope a native speaker helps with this question. I think it's a nominal sentence. The piel verb מלא would have another mem, correct? Here's a link to that binyan: https://www.pealim.com/dict/1053-lemale/ The adj. מלא takes ב. The reason there is no copula is that there are two nouns (הבקבוק and בירה). Does the pa'al binyan of this verb have a passive? https://www.pealim.com/dict/2701-limlot/ But the adj. is, as you indicate, מָלֵא.