I thought I had a pretty nice hack to solve #1 - I opened the matrix in a new tab of the browser, used Ctrl+F to see for 'P'. This highlighted all the P's with

I thought I had a pretty nice hack to solve #1 - I opened the matrix in a new tab of the browser, used Ctrl+F to see for 'P'. This highlighted all the P's with a different color and then just visually found the biggest looking rectangle. Took about 45 seconds :P