Learn Italian: C'è un guasto, chiami il tecnico e lo risolva subito. - There is a breakdown, call the technician and resolve it immediately.

Because this is a formal command (addressing someone as Lei). With informal commands, you attach pronouns to the end of the verb (which would be risolvilo). However, with formal commands, object pronouns like lo must come before the verb.

Why do the two command verbs have different endings (chiami and risolva)?

Because they belong to different verb groups. To give formal commands, Italian swaps the usual vowel endings. For -are verbs like chiamare, the formal command ends in -i (chiami). For -ere and -ire verbs like risolvere, it ends in -a (risolva).

What exactly does the pronoun lo refer to in this sentence?

It means "it" and refers back to un guasto (a breakdown or fault). Since guasto is a masculine singular noun, we use the masculine singular direct object pronoun lo to represent it.

Is c'è part of the command structure here?

No, c'è simply means "there is" (a combination of ci meaning "there" and è meaning "is"). It just states the fact that there is a problem before the commands are actually given.