The difference that "haben" and "gern" make.
-Wie viele Teller möchten Sie haben? In this example above what is the difference that "haben" makes , i.e. the difference between those two sentences :
-(Wie viele Teller möchten Sie haben?) = How many plates do you want?
-(Wie viele Teller möchten Sie ?) = ???
And in the answer below :
=Ich möchte gern zehn Teller.
What is the difference that "gern" makes, i.e the difference between those two sentences :
-(Ich möchte gern zehn Teller) = I want ten plates.
-(Ich möchte zehn Teller) = ???
"ich möchte gern 10 Teller" = 'i would like (to have) 10 plates' is more polite/ formal than "ich möchte 10 Teller."= ' i want 10 plates'
"wie viele Teller möchten Sie haben"= 'how many plates do you want to have' is more formal than "wie viele Teller möchten Sie."= 'how many plates do you want'
you can make it even more formal by adding both:
"ich möchte gerne 10 Teller haben"
"wie viele Teller möchten Sie gerne haben"
btw. it does not matter if you are buying them for yourself or for someone else. none of the possible options implies anything related to that.
It is like the difference between "How many plates do you want to have?" and "How many plates do you want?" Perhaps I am at a store to buy these plates and the store clerk wonders whether I want 8 or 12 or just 4. The first question implies that I am buying them for myself. The second should be used if I had already said that I am buying them for a gift for someone else. Either could be used if you figure that the person will have the plates before giving them as a gift and really most people use the second as it does not imply what you want them for. In English, if you put stress on the word have, it can show impatience with someone who is taking a long time to decide, but you could do the same by putting stress on the word "want". Although by stressing "have" you are stepping around the issue of what they want if they clearly don't know what they want and trying to get them to think practically. (Are you going to have a place to put them? A store clerk should never do this as they want to sell you more than you need, but your significant other might.)
The second is the difference between. "i would like ten plates." and "I want ten plates." which give a different nuance to the same thing. "gern" reminds me of "gladly" but translates to "like" and is always used with a verb. So, "ich schwimme gern." is "I like to swim." ' It doesn't make sense in English to say "I like to want...", so it is translated as "I would like" or if you added "haben", "I would be happy to have..."
So there is the difference from an English view. There may be further nuances from a native German, because which ones we use more might be different from which Germans use more. For example, "I would like" is used as a polite form much more often then "I want", but I think that in German "I want" is fine to use.