What is the warmest place on the Martian surface? What temperatures are seen there? (day, night, seasons, etc.)
I am asking about weather; not anything out of the ordinary such as a volcano.
This is a bit tricky to answer, as we don't have perfect global weather from Mars. But as can be seen from the images at this site, it will be a low lying area near the the equator. If I had to venture, I would say the sourthern part of Syrtis Major, but I haven't seen a high enough detailed graph to definitively answer this question.
What is the warmest place on Mars during the night ?
Probably Badwater crater in the Hellas basin.
With an altitude of -8180 meter, it is in the lowest region within the lower latitudes of Mars.
So it has the highest concentration of CO2 and thus the warmth of the Sun during the day, will be kept there the best at night ?
Depends upon the time of day. Highest temperature ever measured is at the summit of Arsia Mons, about 305 Kelvin (89 F), but it drops below 150 K (-190F) every night.