I’m mighty sorry that I’m the first to address your question, as I know it’s been up for a few hours and that time is really of the essence, especially given the nature of your questions and the lateness of date.
If I understand you correctly, you are showing us the state your shooting mechanism currently is in, and telling us that (1) it is too wide to fit within the perimeter of the robot, and therefore would need to be “deployed” to the sides once the game started, and (2) you currently have no method for holding the ball before being shot. You haven’t addressed wether you have any of the other critical systems already in place, such as picking up a ball from the ground, but given the other things you said I’m skeptical that such things have been addressed by your team.
If I’m wrong, and your team already has a ball intake, your drive base is complete and fully functional, and the only things you need are what was listed, then perhaps you could deploy using pneumatic pistons that push your system components on slides (such as heavy duty drawer slides) to a pre-set end, where they latch in place. A ball holding mechanism could be as simple as a hoop of bent EMT pipe, or a sheet of Lexan, though from your description it’s hard to know what you might need. You would need to do research, and prototype with available supplies until you had something satisfactory.
My fear, though, is that your team needs much more than a few ideas. If you really are still in the early prototyping phase on a major mechanism, and are missing other key pieces entirely, you need to rethink your plan going forward. It will be very difficult to come up with unique mechanisms, and integrate them into a working system, with so little time left. I highly recommend that you look at the mechanisms for picking up, holding, and launching the ball that were used for the Robot In Three Days build, especially team Boom Done, and see if you think you can add such systems to your robot. If you do, then start immediately to design and build, and plan on working long evenings from now 'till Tuesday. If you don’t think these ideas are feasible, then I would (a) complete the drive base, making sure it is robust; (b) create a mechanism that can control the ball without picking it up off the ground (i.e., roll it with your robot), and which can let go of the ball in order to pass, and integrate this into the drive base; © build bumpers that comply with the rules; and (d) get as much practice driving as I possibly could in the next 4 days.
Please consider with your team, quickly and carefully, your path forward. You don’t want to come to next Tuesday and find yourselves without a robot that can do anything! Make sure your robot is built within your means, and that it can (at the very least) drive well, and consistently hold and pass the ball. Good luck.