Learn English – difference between “work alongside you” and “work alongside with you”

Simply "I'll be working late" would be understood that way.

"I'll be working overtime" would also apply, though overtime generally only covers extra hours that are done for extra pay, and not if you get paid a fixed salary regardless.

Yes, both are used correctly. In both cases the "like" could be replaced by "as if". Both are somewhat colloquial expressions and might not be used by every English speaker.

As you say, the first use is sarcastic, meaning "I really don't need any help from her," with the strong implication that, in fact, she would either be completely unhelpful or possibly that she would make things worse.

The second is much less sarcastic. It says instead, "I think I can do this without her help." The implication is that you feel someone has challenged your ability to do something and suggested that you might need help from someone. "No", you respond, "it's not like I need her help! I can do it myself."