Hm, I'd need to look closer but my first thought was 'it's putting out roots'.. Since the last picture looks like some type of jasmine vine, that's a possibility.
Tia, you might want to lay that cutting with the white stuff on it down on some damp soil and see if those things grow, or if they suck the life out of the cutting and then everybody dies. If they grow, they are roots or tendrils for grabbing onto the trellis. If the whole thing dies, it's insects. You could also try scraping a couple off with your thumbnail and see what happens.
I'd look at them closely, if you have a magnifying glass, use that. You'll be able to tell a lot more about them.
