For me, the amount of cloud cover, tree cover, combined with phase of the moon is the single biggest factor is the speed / quality of my night hikes.
When there is a decent amount of moonlight I find that I go nearly as fast at night as I do during the day on well maintained trails. I don't watch / see the trail as much as see where the edges of the trail are. Note: I have very sure-footed and recover easily so not seeing exactly what I am placing my foot on isn't normally a problem. When there is reasonable moonlight (maybe 1/3 without cover) I can more reliably follow the trail by moonlight than with any headlamp. I also found a bright light + GPS with preloaded route could keep me moving close to daylight speeds. I should note though, that I am not a speedy hiker.. 2-4mph depending on the terrain. If I am traveling somewhere at night were foot placement is really important then my speed drops to maybe 1/2 normal plus periodical "where did the trail go?" This is typically because the trail made a turn but there was "a path" which continued straight. In the daylight it's easily to see this sort of thing. Typically it does not take me long to figure out and backtrack.
When going off trail I found somewhat challenging without using a 30 lumen or brighter light for getting around, and brighter with a long throw when there was something tricky wayfinding required.
On the red vs. white debate… I have little to offer. I have never had a red light that was bright enough to be of much help.
I would generally suggest either a hand light or mounting your headlamp someplace down near your waist. Much more effective than the light source coming from the same location as your eyes.
I have come across more wildlife at night than during the day. As to the added danger… it would depend on what animals are in your area.
–Mark