Do player trends stay consistent? in other words if a player improves +3/+1 for example, will he continue to trend up? Or does it vary? Same for down?

Possibly, but it's hard to tell from just one training camp (especially if it's as small as that). Over a season or 2 you should be able to deduce some more accurate trending. If you have a player that moves more than 5 points in TC then you probably have a good indication of his trending.

So there is variable movement? Up then down or vice versa? Also what actionable factors can affect this. Playing time?

Each player has an assigned trend direction, but the movement is random. It's just a normal distribution random movement with a pre-assigned mean. The mean itself is normally distributed with a mean of zero, so 60% of the players generated will have no significant movement, whereas 3% will wildly boom or bust.

I seem to get the 3% busts ... lol

That was me in 13 past draft. I got all of the 3%...