To start with, Time Machine backups take up as much space as they need to, limited by time and how much data is on the drive.
At minimum, they'll take as much as the amount of data you have stored, plus a little. Past that, they will continue expanding to keep a copy of all changed files in increments of hourly backups for the last 24 hours, daily backups for the past month, and weekly backups for everything older than a month. If the Time Machine partition runs out of space, it will start automatically deleting the oldest backups as necessary.
It's pretty efficient, but how much space it will take up depends entirely on how you use the computer--if you only do web surfing, email, and text documents, the rate of increase will be very small. If you're constantly editing video or adding and modifying large photos, it could bloat quite quickly.
My personal rule of thumb is to leave about the same amount of space as the drive I'm backing up, but that only works because I try to keep the boot drive no more than half full, and I store most of my large media on a separate drive backed up with a different tool.
As for your main question: No to both. As you gathered, Time Machine won't officially back up to a directly connected NTFS volume--it requires HFS+. You CAN do some unsupported modifications to allow it to back up to other filesystems, NTFS included, but it's a bad idea in my opinion--I've heard of occasional issues while writing to NTFS volumes via the 3rd party tools, I've had problems myself once or twice, NTFS access tends to be slow with the drivers I've used (which would be annoying given that TM runes every hour and can do a lot of drive access), and even if it worked smoothly you're sort of asking for trouble with your backups using an unsupported configuration. And of course the moment it decides to go haywire will be the moment you actually need something.
Changing the format of an NTFS drive to HFS+ without erasing it also not possible, and again, even if it was, if you don't have a backup of the stuff on the NTFS drive you're asking for trouble if something goes wrong with the process. And if you do, you can just reformat and copy over from the backup. Note, also, that Time Machine is going to work best with its own partition to write to, so I'm guessing here that you'd be splitting your external into, say, a 300GB data partition and a 200GB TM partition, or something similar. Which will work, again with the limitation that the data partition has no backup.
If the data on your external is at all important, I'd just spend the extra hundred bucks for a second external of at least 750GB (I'm assuming here these are 2.5"; if you don't mind a 3.5" you can get 2TB for around $100), then divide it into data backup and Time Machine partitions. You might also use the opportunity to reformat your external to HFS, if you don' t intend to use it on a Windows machine anymore.
