For the NST Manager SmartApp notifications, no. Post in the official thread for NST Manager. If you follow that thread you will become aware of any issues that my be transpiring and reported by other community members as well. In the case of the annoying updates available, there was an issue the last couple of weeks (over the holidays) which others reported as well and that has since been fixed if you update to the latest and greatest code. They thought it was fixed once (right around the time you posted there), but there was an oversight.
Use the official thread moving forward. You can always do a search and then specify that specific thread to search only and look for the issue ie “update available” and you will see postings for it. Anyway that got fixed a couple of days ago so update to v5.24. Those Notifications will go away. Moving forward, if you ever have an issue with NST Manager, post here. There is no need to create another topic 
[BROKEN] NST Manager v5.0 (Does Not Work Anymore)
As for the other notifications and filtering and asking for a new feature, see replies above.