You don't do this! Sounds like part of your problem is not understanding how to shift, and I do not intend to offend with that statement. You do not go directly from the small cog to the large cog without shifting the front derailleur in the process.

As for the brake squealing - toe in your brake pads, ensuring that the front of each pad touches the wheel rim first but only just barely. If the front does not touch first, both squeal and shudder are possible results.