Hi there.. I usually cut the lower tiny branches, even with autos, so the plant can concentrate its energy into creating bigger buds.. the small buds (often called "popcorn") are usually not so liked by many people and often not very dense..
when it comes to bloom-boosters, or bloom-nutrients in general, i would wait until the plant has finished growing in length, and started putting their energy in bud-creation.
In the beginning of flowering, the first weeks, they will still go through a strong stretching-phase.. because of this stretch, they will still require some Nitrogen, which is something most blooming-fertilizers lack (as high amounts aren't wanted during the budding phase).. Once you see she's not getting any taller, but the buds are getting bigger, then it's time to switch and add the booster.
happy growing