Would i be too simplistic in assuming that the radar for the iron dome is probably a higher resolution lower range version of something like the green pine?

It uses the custom-designed IAI Elta Systems EL/M-2084 multi-mission radar, which is thought to exploit technology developed for the EL/M-2080 Green Pine. The two radars operated in different frequency bands.

Also would it be far fetched to believe that they have not gone for goal keeper or phalanx because of the prospects of having stray bullits in a high density population area?

Used in the land role, gun does not fire the solid depleted-uranium or tungsten projectiles originally developed for naval CIWS use, but an exposive-filled projectile fielded with the self-propelled Vulcan air-defence gun. This self-detonates at maximum range.