Learn Swedish: Vi hör gatumusikanten sjunga framför bageriet. - We hear the street musician sing in front of the bakery.

Because of the verb hör (hear). Verbs of perception, like höra (to hear) and se (to see), work just like they do in English when followed by an object. You say "we hear him sing" (not "to sing"), so in Swedish, you use the bare infinitive sjunga without att.

How is the word gatumusikanten formed? Why is it gatu- and not gata-?

It is a compound word made of gata (street) and musikanten (the musician). When a word ending in -a becomes the first part of a compound noun, the -a often changes to -u. So, gata becomes gatu-, giving us gatumusikanten.

Could I use inför instead of framför to mean "in front of" here?

No, because framför is used for physical location (physically standing outside the bakery). Inför means "in front of" in a more abstract or figurative sense, like standing before a judge or performing for an audience. Since we are talking about a physical place, framför bageriet is the correct choice.

Why does the word for bakery end in -et (bageriet)?