How to backup original firmware and personal data before firmware change? Before I try a custom-built firmware, I would like to backup the original one from my 2.1 SE Xperia phone. I know some original firmwares are out there to download but I would trust my own one better. How can the original firmware be backed up?
Please check the backup tag wiki, which already gives you some "first-aid" advice. Take a closer look at the Nandroid section, as that is what you will need:

First, you will need to install a custom recovery (see e.g. recovery-mode). The most common choice here is clockworkmod, as it is available for most devices. Depending on your device, there might be other choices available. For your Xperia, there probably is no Amon Ra Recovery (which is very similar to already mentioned ClockworkMod recovery), but there might be e.g. twrp. This custom recovery will replace your stock-recovery, and add some useful functionality -- one of the new features being nandroid backups. Your device-firmware will remain untouched when you flash the custom recovery.

Once you've installed the custom recovery, you can boot into it with a special combination of keys. On most devices, you need to hold the Vol - and Power keys pressed simultaneously on boot, until the recovery menu appears -- but that key combination might differ for your device (and the custom recovery chosen). Check the documentation/readme/hints where you downloaded your recovery.

Bootet into the recovery, there will be a menu item for backup (it may be labeled "Backup" or "Nandroid" or "Nandroid Backup", but you will unmistakenly identify it). Here you can create (or restore) a nandroid backup, which includes an image for each of your device's partitions (i.e. all that would be touched/changed when flashing another device-firmware; it will, however, not backup/restore your device's radio-firmware).

 
Examples of ClockworkMod (source: XDA, LaptoppMag)

The screenshots show you the ClockworkMod menu of two different versions (I marked the entry you will need to create/restore backups). The first screenshot shows a complete Nandroid backup being made, and you can see in the light-gray test all the "Backing up" lines, indicating each backed-up partition.

Having created such a Nandroid Backup, you can return to this state of your device-firmware anytime. It would also include your apps and data; so if you don't like the custom ROM you've tried, simply boot into your custom recovery, and restore your backup.