Have we ever observed fertile offspring with a different number of chromosomes than the parents?
[..] have we ever observed a situation where the offspring of meiosis has a different number of chromosome pairs than the parents, the offspring lived, and the offspring was not sterile?


Yes!

While it may seem a detail, the difficulty is to know what exactly you mean by observation. Chromosomal abnormalities, gene duplication, chromosomal duplication, robertsonian translocations, whole genome duplication are not super common but common enough to be seen repeatedly. We see them happen again and again in different lineages, we can even investigate how our environment affect such chromosomal abnormalities (Merkatz et al. 1984). So below, I am citing a few papers that I more or less randomly selected among the decently large amount of work on the subject.

Chromosomal rearrangements are sometimes involve in speciation (Rieseberg 2001).

There are many genetic disease in humans that are related to such chromosomal duplication (e.g. Down Syndrome) and de novo mutations for these mutations, while rare, are not so rare that we can witness them only on geological time scale (Veltman and Brunner, 2012)

There are soo many articles on the question that I don't really know what to cite. Of course, there are reviews that can be of interest to you (such as Zhang 2003). I tried to find a video showing a meiosis leading to chromosomal duplication but unfortunately, I have failed to find that.

The mechanisms of these mutations leading to chromosomal rearrangements are pretty well understood. You should probably start with wikipedia > gene duplication # Mechanisms of duplication for an intro.

As you talk about the difference between the number of chromosomes in chimpanzee and humans, you might want to have a look at the post Evolutionarily speaking, why do humans have 46 chromosomes where it is explains (with plenty of citations) how did the change in chromosome number occurred in our lineage.


  I have read a lot about the idea of evolution


I do not want to seem pedantic but given that the vocabulary that you are using (change in kind,  concepts of transfer errors, concept of gradual change) it really suggests that all you read comes from the creationist propaganda and not from the evolution literature. Indeed nobody use these terms in the research. Those terms are mainly used as straw man from the creationist propaganda.

There are many free intro courses to evolutionary biology. You might want to have a look at Understanding Evolution by UC Berkeley.