WebUI on root causing Rest API issues?

We run the WebUI on our root server. I have noticed that during the day when we have users using it we have issues with a separate process that accesses the Rest API. I was just putting 2 and 2 together and was wondering if:

The WebUI uses the Rest API and if a user was accessing something in the WebUI if that could interfere with accessing the Rest API? We have what can only be described as timeouts in the Rest API (basically it is ignoring requests to it) until “after hours” when I think the service desk stops using it. I have a support ticket open for this, but this question never occurred to me until today. Thoughts?

Also is it a best practice to run the WebUI on a dedicated server, especially when using other processes to access the Rest API?