1999 Ford Contour intermittent starting and loss of power

1999 Ford Contour 4 cyl Automatic 97,000 miles

Hello! I have two separate, but perhaps interconnected problems with my ford. The first started when my check engine light came on, and I took it to the mechanic since I also needed an oil change. They ran the diagnostics, told me it was a sensor that was tripped, and then proceeded to tell me to ignore it. Twice when I have attempted to speed up onto a major highway, the car hit 40mph, started shaking and then decreased speed to 0mph. I had to stop and once I got started again, it went fine. An aquaintance had a similar problem, and the mechanics changed the O2 sensors in her car. Could this be the same problem? Also, the last two days (mornings), the car hasn't started. It will crank, but not turn over. Then, by the time it warms up outside (around 10am) the car will start perfectly fine. I had the same problem a few months ago, had it towed and the fuel filter changed, and they said that they could not replicate the problem. Could my fuel pump be failing? What types of questions should I ask the mechanic when I bring it in to be fixed? Thanks for your help!