This is my disk partitions.
Disk /dev/hda: 60.0 GB, 60011642880 bytes
255 heads, 63 sectors/track, 7296 cylinders
Units = cylinders of 16065 * 512 = 8225280 bytes

Device Boot Start End Blocks Id System

/dev/hda1 * 1 1559 12522636 7 HPFS/NTFS
/dev/hda3 3985 3997 104422+ 83 Linux
/dev/hda4 3998 7296 26499217+ f W95 Ext'd (LBA)
/dev/hda5 3998 7166 25454961 83 Linux
/dev/hda6 7167 7296 1044193+ 82 Linux swap

How do I create several partitions (one for FAT32 and the rest for a new linux installation) between hda1 and hda3?

The easiest way without using fdisk, ntfsresize, etc is to get boot it from www.terabyteunlimited.com . Create the boot disk and boot from it. At the menu, hit escape or cancel (don't remember which) and proceed to the partition work dialog.

The interface should be very intuitive, so you should be able to repartition without much trouble. However, I wouldn't recommend that you create an ancient FAT32 file system unless you really need to have write access to some files from both Windows and Linux. There are drivers that can write to Ext2/Ext3 from windows albeit unsafely, and NTFS write access should eventually end up in Linux.

Caveat:

Windows doesn't like moved or resized partitions. Symptoms that I've experienced are hanging during uninstalls and windows hanging before the login screen. Before you boot windows XP on a partition that has been moved or resized, you need to do what the boot it manual says: clear some boot signatures and delete the keys in HKEY_LOCAL_MACHINE\SYSTEM\MountedDevices.

You can only create 1 partition between hda1 and hda3 i.e. hda2. That is because there is the only remaining free primary partition ID available. In addition your extended partition is also completely allocated and so your unable to create additional logical partitions.

To create more then one partition you will need to resize the extended partition. parted or QTparted are the linux utilities for resizing and moving partitions.

To clarify my understanding:
First I create one partition between hda1 and hda3 i.e. hda2 with some free space left (x).
Then resize hda3, hda4, hda5 and hda6 to use the free space x.
Finally create the new partitions hda7, etc.

This is quite weird. What do you use for partitioning? I'm using QTParted or ntfsresize and never experienced the problems you described :-o

You want to resize hda4 i.e. the extended partiton to encompass the free space that way you can create more then one partition.

The only partition tools I've used are fdisk, ntfsresize, and boot it. When I deleted the recovery partition on my desktop (the first one @ 5gigs) and slided the windows one to the front of the disk, Windows XP hung at the login screen. I had to slide the file system back and then delete those keys and clear the boot signatures before sliding it back again.

The same thing happens when I shrunk the Windows boot partition. I don't think you get this problem when you enlarge a windows partition.

I see. When partitions are moved or rearranged then the described problems can happen, I agree.

When partitions are resized then they aren't moved (start position stays the same, at least for QTParted and ntfsresize) but the partition order can change if it's done on a logical partition by e.g. fdisk, you use. In these cases you can fix the partition order by entering the expert menu and using the 'f'' command (fix partition order).