No, much of what you describe is not normal. My 1 month old nx8220 does not have any battery or power issues.
The icon behaviour in the Notification Area is notoriously inconsistent; that's part of XP's "character" which many of us have to put up with. It's not necessarily the fault of the program or service in question.
I cannot say for certain whether the charging pattern that you describe is normal, but I expect that it is. If the capacity is around 95%, it does not really need to be charged. Lithium-Ion cells are best treated a certain way click here and that is likely to be reflected in the charging patterns.
To put your mind at rest, contact the HP technical support line and explain your concerns accurately and in detail; they are very helpful in my experience.