I use Round Team to retweet for me.
However, does Round Team send out new tweets? By that I mean, if I was to make a list of tweets, would Round Team send them out daily for me.
No, RoundTeam doesn't have the functionality that you've described. RoundTeam's main purpose is to curate relevant content to your Twitter Timeline according to the criteria of your choice.
Please, let us know if you have more questions.