Manual Transmission Shifting Advice Needed

[tlr3715]

The 370Z I purchased two weeks ago is my first manual car, and I'm enjoying it a whole lot, but I need some advice.

When I see a red light up ahead I've been shifting into neutral (from whatever gear I am in) taking my foot off the clutch and coasting to a stop. Then shift into first when the light turns green. My friend told me this weekend that I should be down shifting through the gears down to first before I put it in neutral, claims if I don't I could mess up my syncros. Any truth to this?

If there is, does that mean I should also not be skipping a gear when accelerating? I usually accelerate hard through third, then just been kicking it to sixth when I get up to speed.

I also grinded a gear for the first time going from first to second today. Thought I had the clutch pressed in as much as I usually do, but I guess not. Grinded for about a half second before I backed it off of second gear. How badly does this damage the transmission?

Any advice would be greatly appreciated.