I am responsible for delivering different final product/service requests to Team A (usually Customer Sales, Business Developers, sometimes the CEO himself) using in-house-built Software that is developed and maintained by Team Z (Software Developers). As the main user of the Software I am also responsible for testing it for bugs and suggesting changes and features to the software product owner/manager, who decides what can be implemented or not, and when. The changes or features I suggest are based on my judgment and interaction with Team A and their different types of requests.
There are two types of situations where I feel I am not in control and yet I get unwarranted pressure:
There are service issues in the hardware/servers/systems that supports the Software, sometimes completely unexpected and outside normal hours, yet I am still given pressure to deliver the product/service to Team A. The Software Developers however are working on something else (they have other projects/deadlines) so cannot help me immediately.
Team A sends completely new types of requests that according to common sense should be supported by the Software, because they are similar in principle; but when I try them they turn out not to be supported, and sometimes even break the Software - again requiring the intervention of Team Z.
In either case I think the best I can do is try different solutions and communicate if it worked or not. I have no technical background so I cannot actually solve any of the issues by myself. However, I am often reminded of deadlines, asked about estimated new delivery times, etc.
What makes things worse is that often the requests are made after the people in Team A spoke with the software product owner/manager (who is also my direct supervisor), who approves the requests and says they should be possible... but they aren't.
There may be multiple issues in my story, but the common thread is that I am given pressure to deliver and I am not not in control. How can I handle this kind of situation? What is the most professional response?