the load speaker gets its power from touch connection on the Lighting port flex cable . there are two gold pads that need to make contact with the speaker for it to work. i would try opening the phone and holding down on the speaker and see if you get sound. might not be installed correctly. Hope this helps.
i would recommend to try and do a backup and restore on your phone. if there are any apps installed that are draining your battery that will take care of it. good luck
usually with older tvs their wasn't a picture size adjustment. if you have a cable box then you can try and change the video settings on your cable box. more than likely that is set to widescreen when it needs to be set to 4:3 . good luck :)
the bottom mic is out. you will need to replace the bottom charging port as it is all one piece. here is a link :) http://www.ebay.com/itm/Nokia-Lumia-1520-Charging-Charger-Dock-Port-Micro-USB-Connector-Mic-Flex-Cable-/171481488704?hash=item27ed17dd40:g:6F4A...
chances are that the digitizer suffered damage from the drop. if you can see the screen or can hear the phone turn on then a screen replacement will solve your issue. hope this helps.
there may be two parts that need replacing. the top speaker gets its connection from a flex cable that also has the front facing camera and a few sensors and is a quick fix. the mic that you talk into is at the bottom and that is attached to the charging port and Headphone jack. luckily the parts are cheap. Best of luck.