Those sentences are absolutely correct when you omit the pronoun. When you do that, you repurpose the preposition as an adverb. So, in the sentence "The senator voted against" against acts as an adverb to modify the verb "voted". The same is true with #2. Although an English word may have a preferred usage, words are often repurposed. For example, nouns can be used as adjectives and vice versa. Likewise many prepositions can be repurposed as adverbs. Be careful when you do this though. You have to be careful lest you be misunderstood. If you do use a preposition in #2, consider using "one".

Informally it’s possible for native speakers to ‘vote against’ and ‘live without’ without explicitly stating the direct object, but only if the meaning is very clear from the context. How are you voting? I’m voting against. Do you like having Alexa? I can live without. But some people won’t like it, and if we heard it being said with a foreign accent, we’d likely see it as a sign of weak English.

!Hola, Hernadez! To answer your question, yes! It would sound weird if you do not add the pronouns at the end. The English language really relies on having clarity on who or what you are talking about, especially when it comes to the object of the sentence without prior context. I hope my answer was helpful! Buena suerte and I hope you have a wonderful day! ❤️