But LHR definitely isn't one of the airports where I would end up paying those extra departure taxes, right?

I'm not so much worried about getting lost and missing my departing flight. I have started looking around at tours that would assist me in making in back to the airport on time since it is all very new to me.

I am a little worried about luggage since I found a story where a girl left during her layover so they removed her bags from the flight, thinking it was suspicious. I'm not even sure if I need to collect my bags when I arrive at LHR or if they will be put straight through so I should probably find that out. I arrive in terminal 3 and leave from terminal 5...