Congrats on launching your tree climbing activities!
First off I highly recommend using a "pipe" or sleeve style cambium saver, they are very simple to install and retrieve. The saver you acquired is oriented more to professional tree workers. Take a look here:
Rope sleeves
The "Dan House" sleeve is the most versatile. Leather sleeve is good but has higher friction (resistance) compared to the Dan House sleeve and can fight you on the install because it has a relatively rigid "U" shape. Ring-ring cambium savers are also oriented towards pro work climbing, pretty much a major pain in the butt to install from the ground unless everything (limb size and location) is perfect. Sleeve style cambium saver are the easiest to advance when you re-pitch above your initial rope setting made from the ground.
Next... your climbing harness is the most important piece of tree gear you'll own. In technical tree climbing you're going to spend a lot of time with your body weight on your harness. The harness you bought will cause you pain very quickly, within minutes, it has zero waist padding and no leg strap padding. Tree climbing is in a technical way described as "work positioning" climbing, meaning you never have slack in your climbing rope, (except in rare instances), your weight is on your harness 90% of the time while climbing. Rock harnesses and the Petzl Gym harness are designed to catch a fall or for very short duration hangs like riding a zip line. A New Tribe Basic harness for example is sufficient to meet those requirements. Many options from there if you are ready to spend more money. A very good harness is going to be anywhere from $300 up into the $600 range.
-AJ