Learn Italian: Mi sono alzato senza svegliarlo. - I got up without waking him up.

Because the subject of both actions is the exact same (you are the one getting up, and you are the one not waking him). When the subject is the same, Italian uses an 'implicit' clause, which means simply pairing senza with the infinitive verb. If the subjects were different, you would have to use a conjugated verb.

Why is lo attached to the end of svegliarlo, and where did the final 'e' go?

Object pronouns like lo (him) attach directly to the end of infinitive verbs. When you do this, the rule is to drop the final -e of the infinitive. So, svegliare + lo becomes svegliarlo.

Why is alzato used with a reflexive pronoun (mi) but svegliarlo is not?

Alzarsi (to get up) is reflexive here because you are performing the action on yourself (you got yourself up). However, the second action is waking someone else up. Therefore, you use the non-reflexive verb svegliare (to wake) combined with the direct object pronoun lo (him).

Since the sentence happened in the past (mi sono alzato), shouldn't we use the past infinitive (senza averlo svegliato)?