Can Ubuntu Linux be installed on FAT32 or NTFS?

Linux relies on a number of filesystem features that simply are not supported by FAT or NTFS -- Unix-style ownership and permissions, symbolic links, etc. Thus, Linux can't be installed to either FAT or NTFS. (It used to be possible to do this using a FAT driver that adds those features, but it was removed from the kernel years ago because nobody was maintaining it.)

If you need a USB flash drive that both boots Linux and can be accessed from Windows, then I second Zonder's recommendation to create a FAT or NTFS data partition on the drive, along with the Linux partition(s). Note that you'll need to put the FAT or NTFS partition first on the disk, because Windows treats USB flash drives as "superfloppies," and will access only the first partition on the disk. Linux is not limited in this way, so you can put the Linux partition(s) after the shared-data partition. Also note that you can't use FAT or NTFS as the Linux /home partition; if you go this route, you'll need to mount the shared-data partition somewhere else in Linux.

How about creating 2 partitions one for linux os minimal size and then leave the rest as fat32. That way linux gets what it wants and you can stil use the remaining space.

I am not sure how mac os will behave with this but windows is supposed to ignore all partitions on a removable drive except the first windows readable one.

There is a program called bootice which can help you do this. But a quick internet search will find lots of articles on partitioning a usb drive.