- Yes, じゃ here means では. So 最近（では・じゃ） would mean, "as of recent times."
- ながら can show simultaneity as well as contradiction. For example:
Although slowly, I’m approaching completion.
So in your sentence, 恋人の存在を公言しながら would mean something along the lines of "while/although they have announced being in a relationship..."
The も here means "also". It refers to the（恋人の存在を公言しながら活動している）女優 who are "working actresses that have announced that they are in a relationship". This might be in contrast to actresses who announced being in a relationship, and stopped working as one. It might also be in contrast to actresses who are unable to be in a relationship because of their job.
Putting it all together:
Plus, there are plenty of actresses nowadays that continue to work in the industry despite announcing that they're in a relationship.
Also, is this 押しの子? I feel like I've seen this somewhere.