What's the convention in writing Chinese words and names with English letters?

Well, it's a bit hard to answer your question, but I'll try it.

For Q and X, they're basically short forms for a type of sound that I obviously can't express easily on the internet. For example, for the word 'quan', if you were to pronounce it, it would be something close to choo-an, the two syllables said really quickly to make it one syllable. 'choo' as in the pronunciation of chosen and 'an' as in ban. As for 'x', it's like the same thing but a different sound. 'xuan' would be like shoo-an. Same 'an', and the shoo is pronounced the same way as the english word 'shoo'.

For vowel pairs, we pronounced the first vowel first, then the second. For e.g., 'liu' would be 'lee-oo', again said really quickly such that two syllables become one. 'lee' would be the 'li', and 'oo' would be the 'u'. For 'leung', it would be 'lee-ung' - that one is pretty obvious, same way, diff example.

Hope my answer helped!