Hmmm I need some input

So my boyfriend dumped me this past Thursday (Nov. 10th) and during that he said I want you to still be in my life and all that even though he's wanting to see/start a relationship with a new girl.

He said I'll give you some space

But he has been texting me everything single day since then. Saying how he misses me and how he wants to talk and doesn't want me to be sad because he thinks I'm beautiful and that I mean everything to him and I get a whole lot of hellos and heys

My best friend (who is fully aware of my breakup and all) said do not respond to his texts. He missed out. He made a choice. Do not respond for at least 1 week. Because in a week I should have cleared my head a little better and have better judgement on how to respond as oppose to answering with raging emotions.

So I have 2 questions. Would you remain friendly with a guy who dumped you (a few days after your birthday) because he'd rather be with someone else?

And should I respond in a week? How should I respond if you think that I should.