Gyrations are no more than the days upmoves and downmoves. I would count the YM yesterday as 5 and half gyrations .. up, down, up, down, etc (one up/down or one down/up being treated as a gyration). The number of gyrations which show to you, depends on the charts/bars you are using .. less if slower half hour bars or say more if faster five minute bars apart from using other choices such as range, tick or volume bars of faster or slower 'sizes'.
there is one thing and one thing only that moves price an inbalance in supply and demand period trends are just a way to model periods in time where demand outstrips supply. over time these are just models. asking if trends exist? of course they do. but it's merely a model of past action the majority of the time, markets are not trending vertically, they are trending horizontally, to paraphrase market profile terminology. that's how i see it
no, those oscillations are based on specific range parameters at both extreme and minor levels. Those green line oscillations on price are the extreme oscillations for trade entries. The lines on the indicator verify and confirm Primary Trend. The minor oscillations are trading opportunities in-between Primes.