Couple of tips for both of the new climbers.
1) when tied into the tree make sure you are around a strong, healthy limb or around the trunk itself.
2)unless you want to buy a new saw sooner than later always keep your saw attached to you. If you can't reach the cut, reposition. Its also helpful when you need to drop the saw and hold on for the ride.
3) Its a whole different beast using a saw in the tree compared to using it on the ground so always use your lanyard, buckstrap when making a cut. It only takes a split second to cut your rope.
4)As much as a top handle saw seems like a saw for one hand, its not. If you can't reach, reposition. If you need to hold a limb, cut with your chainsaw 3/4 of the way or so and the rest with your handsaw or tie it off. The saw doesn't know or care about the difference between your hand and the tree.
5) Take your time, speed will come with experience.
6) NEVER use your climbing line as a lowering or pull line. Remember, your life is hanging by that line that your dropping trunks on or shocking with a load.
7) Inspect your gear before a climb, especially your rope. You don't have to go crazy doing this, just a quick check of all the key points and running your rope through your hand and flaking it out (you'll feel the cuts if you have one).
8) Learn the right knot for the right job, practice, practice, practice.
9) Feeling more confident in the tree will come with experience. Learn to trust your ropes and spikes.
10) Remember, each wood reacts differently to different cuts.
Hope this helps a little bit atleast. Happy climbing and be safe.