"You are drinking again!"
They have the same meaning but znowu is a long form and it is used at the beginning and at the end of sentences. The short forms like znów are used inside sentences. Znowu and znów are not the only words following this rule. Here another few examples: Dzisiaj - dziś (today); Tobie - ci (to you); Mnie - mi (to me)
That's not true - znów and znowu can be used interchangeably.
Woah, that's a hard question. I feel the difference, but... "ponownie" just seems to be "again", but it suits some sentences and it doesn't suit some others. I wouldn't use it here.
But I googled a sentence "Gortat znów zagrał dobrze, ale Wizards ponownie przegrali" and while this seems more natural, I probably wouldn't bat an eye if they switched the 'again' words between the clauses.
"na nowo" is more or less "from the beginning", kinda like "from the scratch".
"Po wypadku, musiał na nowo uczyć się chodzić" (After the accident, he had to learn how to walk again"