Advanced Arduino Project Help
Your question is incredibly broad. However:

1. Could I complete this project using Uno and Mega?

Yes, almost certainly

2. Is there a method for compiling data and storing/sending using Arduino?

What? Yes, you can store data onto an SD card using a simple level-shifting piece of hardware like this:



3. What are the capabilities of Arduino?

This isn't a reasonable question (it's too broad). I suggest Googling for things people have done. For myself, I made a humidity and temperature sensor using the same processor as in a Uno. It also runs from batteries.




  ... a very time tight project ...


Time is going to be your enemy here. Learning how to drive a touchscreen, save files to an SD card, interpret RS232 data from your sensor, and make it all work reliably is not the sort of thing you will do in 3 days.

Even if you dumped all your hardware on my desk (and I know how to program Arduinos) I would estimate two or three weeks to calmly get each part going individually and then interface them all together.




  Would you suggest using breakout boards over shields? 


Shields are well and good if they do what you want them to do. A breakout board will have more flexibility.


  because of pin availability would you suggest trying to use the Mega rather than Uno?


Depends how many pins you need. If you use SPI or I2C you can (probably) drive your display with only a handful of pins.

The Uno will probably have enough, and it has the flexibility that you can easily replace the processor chip if you damage it. You can't do that to the Mega. Plus, more code is written for the Uno so you are more likely to find libraries that work "out of the box" for a Uno.

I wouldn't be getting the "more powerful" device unless you have identified a specific reason to have it. For example, some of the faster and more powerful Arduinos (and other boards) with ARM processors may well do more under certain circumstances, but be somewhat harder to use.