1) If “J’en veux plus” means “I don’t want more of it!”, then how do I say “I want more of it!”?

As Luke commented, je n’en veux plus/j’en veux plus is better translated to “I don’t wan’t it anymore”. Your sentence would be je n’en veux pas plus.

“I want more of it” translation can be written exactly the same way: j’en veux plus, but is pronounced differently. The final s of plus is sounded. See When does one pronounce the 's' in plus?

Alternatively, you might say j’en voudrais davantage or j’en veux encore.

2) What are the rules for when I’m allowed to delete the “ne” in “ne .. pas”?

You can drop it in non-formal spoken French.