You can use any size jars you want/have.
There is no need to only fill them half way, why anyone would do so has me stumped.
Fill them right up, even stuff them if you like, this will not cause any issues.
No real need to buy any strips, just jar the flowers when dry, but not crisp an not too soft and spongy. If after opening the jars they have gone too soft again, just leave the lids off for a few hours or overnight. If they are too dry, add a couple of green cannabis leaves for a few hours to plump them up again. Your buds will not magically freak out if the humidity is 5-15% either way than a perceived optimum level.
If you are really worried or OCD, BoVeda sachets in the 67% humidity rating will keep your buds at 67% for as long as their crystals are working properly and they are probably the easiest and a cheaper option than test strips, but you really don't need either.
Hope this helps, Organoman.