That's not true. Assuming you're in level flight, if you increase speed you require a decrease in angle of attack to maintain the same lift.Another big part of the tail plane stall with increasing airspeed is the faster you are going the more lift the wings are producing...
You're correct that an increase in speed will put the nose down, and that's what increases the angle of attack on the horizontal stabilizer.
This makes no sense. It's not clear to me what you're trying to say.More lift on the wings increases the down force (lift) the tail plane needs to create which is made worse since the nose down attitude tends to also increase the angle of attack on the tail plane so it's now required to create more lift (down force) at a higher AoA compounding the problem.