Hi,not to be nit picky but you need to work on your hand placement-having both hands at the bottom of the wheel in a turn means if the rear steps out your going to spin.I try and get my hands so that the leading hand(left hand in a left turn)ends up near the bottom and the trailing hand is around the 10 o'clock position.This way you have nearly a full rotation of the wheel available without having to move your hands.
Brakes are for slowing the car and the engine is for making it go,downshifting too early is harder on the engine,clutch and most importantly the chassis balance.Engine braking means more weight transfer,enough it could cause entry understeer.Pop a crisp downshift only once the car has slowed on the brakes to allow a smooth trasition from one gear to the next,heal and toe is a must.
On the slower corners it looks like your turing too early resulting in running wide and not being able to get back on the power untill you nearly straight.Pick an entry point AND entry speed that allows the majority of the turn to be completed by the apex so the wheel can start unwinding and the power being fed back in.That change alone will results in many seconds coming off the lap time,its the most important thing to get right imo.Besides that most off course excursions are can be traced back to an early entry more than too much speed(well too much speed for that line but not always too much for the proper line).
I included a quick vid of me in my old 100hp honda civic ice racer at the DDT for a time attack.Sorry the vid doesn't show my hands but you can see the downshifts don't upset the car and that most of the time I'm back to the power by the apex.Embarrassingly I shoved it from 2nd straight into 1st when coming up onto the back straight,surprised my tired old engine didn't explode bits everywhere.
http://youtu.be/shokDBdGCYY