These are my more or less candid response to your questions...
1. Most, including myself, seem to experience sub-MOA groups with these rifles, provided the shooter does his/her part. Bottom line, accuracy comes at a price; it all depends on how accurate you want to get -- CZ rimfires are reputedly quite accurate out of the box, and they're typically around $400 rifles. Yet many aren't satisfied with that either, and so there are trigger kits and other mods available for them, not to mention that even the "best" still do better with a bedding job.
For myself, I didn't consider 100 rounds to break the barrel in to be too much; with a .223 it took me about two hours. From what I've read elsewhere, including sites like
www.snipercountry.com a 100-200 round break-in is to be expected for any rifle. I suppose a larger caliber with more recoil might require more trips to the range. But even with that, consider that ANY mechanical device requires some sort of break-in, regardless of how well machined it is.
2. The triggers are stiff, but I've found mine easier than most as far as factory rifles go. Trigger weight, I believe, is a response to litigation issues. Some rifles come with "adjustable" triggers; H&R/NEF doesn't make any as of yet. If you're getting another barrel, however, you can have the factory lighten it for free when they're fitting the new barrel. Keep in mind, gunsmiths exist for a reason, and it isn't for any one brand of rifle.
3. Some rifles do have issues with this; most are solved by a good cleaning, though there are other fixes as well. In my case, polishing the chamber consisted of wrapping a piece of cloth around the tip of a cleaning jag and running it along the chamber for about 20 min. while watching TV. After 2,000 rounds since, it stuck once, and that was because I was wondering how long it would tolerate going without cleaning.
4. I've not had this happen with the .223 or .17HMR, but these are not heavy loads. Others may be able to give advice regarding this, but from what I've read, a good thorough cleaning can fix most of them.
I believe the H&R/NEF's to be very good rifles. While they don't come with some of the features more expensive rifles come with, they do what they're designed for very well. I've read other forums for other types of rifles, and ALL have their quirks. I've inspected $700+ rifles at the local gun shops, and some were set up very poorly, including actions so stiff you could barely work them.
The H&R/NEF, in my experience, are reliable and accurate, and will put up with a lot of abuse. It's up to each individual to decide what they want, and what they're willing to pay for it. In my case, a better trigger is the only modification I'd consider, yet I'm already shooting close to my limit with them already. Either way, paying $200 for a good rifle and adding $50 or so for a trigger job is still less than $400 out of the box, and leaves me with more money I can spend on a good scope.
Good luck...
Just my $.02...