The words "more" and "much" has to do with quantity. "More" is a comparison. "I have more water than my brother." "Much" is a large amount. "I have much water" but "much" in this context is a little unusual. It would be better to say, "I have a lot of water" (a lot instead of much). I would prefer to have tea. I prefer playing games. Hope this helps. :)

But I think I would prefer saying it with the 'to have' form.

Ah! And you could say, 'I would prefer having tea....' in a conditional sense. I would prefer having tea in the garden, if only we had a garden!

You can say - I prefer to have tea or I prefer having tea. It would change the meaning a little - so what exactly do you want to say? I would prefer tea, please. Thank you, you are so kind. (And then you drink your tea!) Or, do you mean, I prefer having tea in the garden in the mornings (rather than in the dining room). This last sentence could also use the 'to have' form.

You could say - I have much more water! I have much more water than I had before.