Were I to eat at a Japanese restaurant in the heart of NYC,
i am sure that if I used regular US table manners, my hosts would be
unsurprised and uninsulted.  No one would mind.

But it might be extra-special to use some proper Chinese etiquette to
honor my hosts.  What's a proper way?

A great answer would address all of the following:
I'm told I should never refill my own tea or sake.  True?
Apparently, there are clear levels of politeness in Japanese language.
 If I were speaking in English, how could I convey my thanks to the
chef for a wonderful meal?  and how could I respond if it's terrible?
Should I leave some food on my plate, to show that I'm full, or eat it
all, to show it was good?
How fast or slow do I eat?  
etc., etc.

I did some searching around and found the most unique links without
giving the same things.

Here are some links that you may find useful: (dig around) 

http://www.geocities.com/japanfaq/FAQ-Manners.html
http://www.japan-guide.com/e/e2005.html
http://www.frommers.com/destinations/japan/0229032805.html
http://www.shejapan.com/jtyeholder/jtye/survival/manner/manner1.html

When answering your individual questions:

These links provide some Japanese ways to convey politeness but
nothing about using direct English words.

Fast and slow, food on the plate... the links share an ample amount of
information.
________________________________________________________________________

Being helpful until the 'real' amswer comes if it does. 

Good day!

"But it might be extra-special to use some proper Chinese etiquette to
honor my hosts".

In a Japanese Restaurant?

Perhaps not.

THe blanket rule for table manners applies here too:  do what your
host does, unless you are absolutely sure that it would be a breach of
Japanese  or US table manners.  Wait for your host to refill his tea
or sake before you do.
Express your thanks and appreciation to your host and let him pass
them on to the chef.  Your host is paying and probably tipping, so it
is his position to deal with the restaurant staff.  For you as his
guest, they are "his servants".  By the same token, you shouldn't
critize anything beyond agreeing if your host suggests that he is
dissatisfied, but then only to him.
Sure, it is nice to agree to his words of thanks, but it would be
impolite towards him if you suggested by using a proper Japanese
expression that you were more knowledgable than he.
If you can eat with chopsticks, fine, if not, that is fine too, and no
one will be  upset if you try and have difficulty  - as long as you
don't splatter someone.
It is easy to practice with a couple of pencils at home.   If you
discover that it  seems hopeless, then you don't have to embarrass
yourself by trying in the restaurant.

(abt the Chineses etiquette)

Woops!  I also asked this question for Chinese etiquette, and thought
I had changed all the relevant info.  I meant to say 'Japanese,' of
course.
so sorry.

If you are eating with Japanese "customers" for example:  Do as they do.  

If you are eating out on your own, do what you want to do.  It's your
right.  You are in America.

If you are eating with others, if you want more tea, fill up their's
first.  They'll see that yours is empty.

Don't go "Chinese" on the Japanese.  Serious insult.

If you enjoy the meal, say thank you, and that you enjoyed it.  If you
can look this up online on how to pronounce it, they will be even more
impressed.  Another way is to ask the server while you are eating, or
when you walk in, ask the hostess.  Typically, they speak English. 
Don't be afraid to ask.