@Fantum is almost right, only that at the time of the snapshot after the ICO, you will get 0,5 Ignis per 1 NXT. The exact date, as far as I know, was still not communicated. I expect it in November.
With respect to your questions:
1. What If I save NXT's on my NXT online wallet (wallet.mynxt.info), will it be good enough to grab the new Ignis coin?
Yes, the web wallet according to what Jelurida members said was supported for the snapshot, because you own your private key. It's less secure than a secured home PC wallet, but you should know that already.
3. What If I purchase NXT coin today and send it to my online wallet, will I get the new Ignis coin or not?
Yes, you will. You can even wait until a couple of hours before the snapshot. Only you should make sure your transaction to your wallet (online or desktop) is recorded in a block, so to make sure you shouldn't wait too long until you buy. It is possible that there will be many "last minute Ignis hunters" and that the blocks before the snapshot will be pretty full.