@YuZhang, I think a lot of these questions boil down to "what questions are you trying to ask of your data", and many of them have been addressed previously on this forum.
A quick search 
for "diversity filter" brings up some great posts, including this fantastic discussion. 
Give it a read!
Below, find a couple of additional thoughts.
You have noticed that making some of your samples invisible does not produce the result you would expect if you made an emperor plot of filtered data.
PCoA results are calculated using all of the samples provided, and each sample's projection on the plot is influenced by all samples in the data, not just the visible samples. As such, you should be careful when making some of your samples invisible. This can be a useful tool for simplifying your view of the data, but must be explained very clearly when sharing results; a PCoA projection of all samples with some of them invisible is not the same as a PCoA projection of only the visible data, and can easily be misinterpreted.
Probably not, but again, this depends on your data and the questions you're trying to answer. Rarefaction normalizes data to reduce bias caused by samples with varying depths (i.e. total counts). This specific method of normalization may not be necessary, depending on your study and what diversity metrics you're using, but some normalization is likely required.