Appropriate to follow up w/ Headhunter?

I am in the process of having / having had the following two conversations with two separate PE headhunters and am looking for some advice:

(1) Email / LinkedIn back and forth on 1/22 (Friday) to set up an introductory call for early next week (25th - 29th) regarding an opportunity. I gave my available times same day and never heard back, and sent a soft follow-up on Thursday (1/28) of this week. Was that an appropriate thing to do? It felt warranted given headhunter's sense of urgency (i.e. setting up a call over the next couple of days)

(2) Had a phone call w/ headhunter on 1/22 (Friday) regarding an opportunity which went very well with me feeling like I made a good impression (knew lots of details about the fund, sold my story well, etc.). The headhunter said they would "keep in touch on this one". The call felt very rushed though (headhunter sounded pretty stressed and was short) and lasted only ~10 min which was strange. A couple days ago I get an email from another headhunter from the firm asking me to fill out my interests on a form that has various PE opportunities (when I made it very clear on my initial call that the first opportunity presented on the phone was the only one I was interested in) It has been almost a week and have not heard back. Would it be appropriate to follow up by early next week if I don't hear anything?

Might be overthinking it but its my first time going through this process. Thanks all.