Mac cannot write natively to a NTFS formatted drives. There are utilities out there you can install that will allow you do to so. One is called Paragon I think.
I've never used it, as my external is formatted for Mac OS X as it never gets used by any other operating system.
Making a Time Machine backup requires a hard drive formatted in HFS+.
Yeah did some research and found out about paragon, i have a question about that, is it seamless, ie does it work with finder(or whatever else the file system explorer on OSX is called, i am not sure that it is finder) or do i have to use a separate software to see the NTFS file systems. Also if i have an external hdd will the read/write speeds be same as on Windows.