Yes, H&R is famous for out of warranty repairs, have him give them a call, toll free, (866)776-9292. But the pop opens on new firearms are usually shooter error, see pop open medicine in the FAQs as well as the Handi Basics 101, oil on the latch or shelf and not closing the action firmly will result in pop opens, so will shooting improperly sized handloads. Trigger jobs are easier than you think, many gunsmiths are ignorant about H&R triggers, but anyone with the most basic handyman skills can do their own trigger job, it's outlined in detail by Perklo and more simply by Raynor in the FAQs, hundreds of first timers have done their own trigger job here. But H&R will also do one to about 3½lbs as long as it's 6lbs or more to start with.
Tim
