2002 vw New Beetle with multiple problems

I have an 02 beetle that i just bought a week ago. On the drive home I started to lose power but it worked ok the rest of the way home. I have my room mate drive me to and from work since I didn’t have insurance that day. I get home that night to check the headlights. When I started the car the whole thing shook like an earthquake and the check engine light came on. I had a mechanic come out and he says I need a new coolant temperature sensor. so I got that replaced but then i go to fill up my gas and it starts to do the thing mentioned above. I got to the traffic light and my battery light and check engine light comes on. this time though the car doesn’t go. so I turn it off and try to turn it on again but only the lights on my dashboard came on. so I get out push the car forward and back, then it starts fine, without any of the lights on. from there on the car started working fine. I unfortunately know very little about cars, so if anyone can help me figure it out or want to just take the car off my hands i would greatly appreciate it.