usa – How shall a pedestrian walk across a busy road?


I have had multiple scary experiences crossing streets and highways with fast moving traffic in US. My impressions are that the traffic system is not designed particularly with pedestrian safety in mind, or it is my ignorance and I would like to learn more.
The following is one of the experiences.

I walked across McLean Blvd i.e. NJ 20 (a state highway), between 18 and 17 St (see Google map and 3d navigation initially looking to the south at the traffic light) , first from the west side to the east, and then back. In both directions, I walked in front of the north-bound traffic when they stopped to the traffic lights. (Walking in front of the south-bound traffic might be another option, but I didn’t realize that).

When I walked back from the east side to the west, the traffic light suddenly turned green (it was red when I stepped into McLean), and I was still in the middle lane of the north bound traffic. Both cars in the slower and faster lanes were started moving, and I had to walk back to the east side, and was scared by the car in the slower lane fast approaching me.

Questions:

Was it a bad decision to walk back? What should I have done when being stuck in front of the middle lane?

I was wondering how to walk across McLean i.e. NJ 20 safely between 18 and 17 St? What signs could I have looked for as crossing instructions?

For example, I noticed there was a fork from McLean on the east side, which merged with McLean at the traffic lights. I saw some north bound cars used it to turn around at the traffic lights. Would it be safer to walk in front of the south-bound traffic than the north-bound traffic, in order to avoid those north bound cars which turned around?
Is there a sign near the traffic lights indicating to pedestrians to cross McLean only in front of the south bound traffic, not in front of the north bound traffic? (There is no sidewalk or waiting area on the east side, which would have helped to guide pedestrians to walk across McLean.)

I just remember that when I walked slightly to the north at the traffic lights, I couldn’t see which light is on, because my line of view is too much parallel to the traffic lights. So I didn’t walk a bit north to cross in front of the south-bound traffic. Sometimes not being able to see or tell traffic lights from certain angles convenient for pedestrians has been a problem for me.

Thanks.