The engine check light flashes and immediately the engine speed dies

My car's antiskid sensor started turning on by itself, first only when turning at low speed but then even when driving straight, causing the engine to stall. I was told to change sensor and even the rear bearings. Finally, a mechanic gave with the solution when he told me there were some loose steering rack rubber bushings.

It has occurred to me that, when driving in hot places and along an uphill uneven road, the car won't go over 50 mph and the engine starts vibrating as if were about to stall. In two opportunities, my Rav did not move any more but the engine kept working. After waiting for 20 minutes, I started driving normally, but still with the problem appearing on uphill roads. After changing the fuel pump, the vibrating of the engine disappeared but the speed still won't go over 50 mph when ascending. Something new now is that, when the car is stopped, it sometimes shakes as if it wanted to stall. I personally believe it has something to do with the fuel system.