nozzle diameter vs heat question

Filament acts like a heatsink if you are familiar with that term. As it flows through the nozzle it pulls heat away with it. So naturally the more filament that flows through or the faster is flows through then the more heat will be pulled away. A bigger nozzle will not fix the issue. Most people use a .4 nozzle. There are two fixes. One is going slower or two is adding more heat. You need enough heat so that during long runs where filament is fed the temp on the nozzle does not drop more than a degree or two.

When was the last time you ran a PID auto tune? This is only possible on an open source machine or a Da Vinci converted to Ramps. But it is a necessary step for proper machine calibration and the heaters on both the nozzle and the bed do need to be calibrated. When you run a PID auto tune it will heat the target and will run some stuff in the background and eventually spit out 3 values. Those values need to be plugged into the firmware in their respective places under the hotend and bed settings. These values control the rate of heating and the amount the temp pis allowed to rise and fall before removing or applying heat.

I don't think 0.5mm will be a problem for heating up. Assuming your heating element is 40W or better. I have been print with 0.5mm nozzle for a long time to save printing time at cost of resolution. The overall strength of print are much better. You need to use different flow rate for different layer height for best result. I would not recommend it if you want good resolution.