Are the attacks being performed using burpsuite detectable? If yes, how should we stay anonymous/secure while conducting web application reconnaissance?
BurpSuite is only used to send HTTP requests in an automated way. There is no way to tell if a request is coming from BurpSuite or not. (Just have a look at your request header or body).
You might be able to detect such a robot though. Tools such as BurpSuite use a scanner, and you can trap them by making them follow an invisible link on your website. Tools would automatically follow the link whereas users wouldn't even notice it. If someone visits the website.com/trap link, you can tell it's a scanner.
BurpSuite is just a tool, attacks can also be performed manually, just think about BurpSuite as a web browser with automated actions to help finding vulnerabilities. (Yeah, I know it's more than that, but all it does is send HTTP requests).