I'm replying to my own first post in this thread, to give an update.
After reading all the helpful suggestions here, listening to the dealer, and re-reading the entire saw manual, I went out today to take down some more buckthorn, using a new chain (same type) with my old bar. I cut trees on and off for about 5 hours. No bent chain links, no chain popping off the bar, did all that I asked it to do.
I think I'll chalk it up to new guy using a chain saw (or "user error"). The dealer's suggestion about cutting from the bottom of the bar right near the saw seemed to really help. I also avoided where I could "limbing" the small trees, using my hand-lopper instead wherever I could. I also tried to make two cuts from either side of the tree to avoid pinching.
All in all, I am satisfied that it was not the saw. It was me.
Thanks again for all the suggestions. I have learned a ton about how to properly use my saw.
Two other worthy points about chain saws.
In another forum, a doctor posted a suggestion to use cutting chaps. I am glad I listened. They arrived yesterday. Today, I used them, and would have had a nasty cut on my left leg if the chaps hadn't stopped the blade. I was cutting a smallish (2") tree, it buckled on me and spit the saw back at me, grazing my leg. The chain got caught up in the kevlar fibers, and stopped. I immediately shut the saw off and then had to take the chaps off to untangle it from the saw. I figured that was a good sign that I had done enough sawing today.
Also, someone in this or another thread mentioned the importance of a helmut. I didn't have one, so I used my bike helmet instead. Good thing. I was taking down several large (40' tall) buckthorns today. They were in an area where they had grown around a large oak tree (trunk diameter of the oak is probably 3 to 4 feet and the branches spread over a good 80 to 100 feet. As I was taking one of the larger buckthorns down, I felled it in a direction of a fairly clear path. The problem was that it was supporting the weight of a dead oak branch 30 feet up. Without the buckthorn as a prop, that branch came down right at me. I saw it coming, but was not able to avoid it entirely--thunk, right onto my helmut. I was braced for it, so I think I'll just have a sore neck tomorrow, but if I had had my Kubota hat on, I would have a nasty bump, or even a concussion.
So, thanks to this forum, I do not have a scratch on me tonight (I also picked up a better pair of cutting gloves the other day, so no thorn scratches on my wrists--Stihl brand gloves, cause their orange).