I work in a mountain site, and getting craggy stones out of permanent beds is a continuous process. In the early phases, many people sift rocks out of special beds using a sifter made from half-inch mesh hardware cloth. In my experience, if the soil is well-enriched with organic matter and cultivated prior to planting to replenish its air supply, carrots will push aside rocks to one half inch diameter. However, if the taproot runs into such a stone, it will make it fork.

From what I've seen (never done it myself), you should be able to root larger cuttings (truncheons) of this plant as easily, or maybe more-so, as smaller cuttings. If there is significant new growth at the tips, you may have to prune back to firmer wood. A moisture tent and rooting hormone should improve your odds.

Just watch head clearance, as in your head.

Yes I would say to cut them down a bit You should try air layering if you want a bigger plant there's a couple nice videos on YouTube where a guy gets a nice 1' plant with branches off an air layer