Calibrate Desire Battery - it worked for me !!

That was the SLCD one.  The other phone only uses the default 4GB card, so I couldn't store a couple of movies and my entire music collection on there.  Sure, I could swap the cards, but I'd rather not open the rear cover unless it's really necessary.

As for what to do with a new phone, I'd suggest the following procedure :

After removing everything from the box, insert the SIM and the SD card, hen the battery.  Put the rear cover on, turn the phone on and and plug it in for a full charge.  
Once the LED turns green, the phone will stop charging by itself.  Unplug the phone and start using it.  
Use the phone (you'll have a lot of setting up to do at first) untill it gives a battery warning.  
Plug it in again and calibrate the battery

Ideally you'd unpack it in the morning.  That way you can deplete the battery in the afternoon and calibrate it in the afternoon/evening.

TBH it doesn't really matter if the phone is on or off on the first charge.  However I did indeed change the text a bit.  Here's why :

Some Desires occasionally have a glitch which causes the LED to stay orange even after it detects that the battery is fully charged.  This glitch only happens when the phone is off, which is why I would suggest turning it on for the first charge.  My HT06 has done it 2 or 3 times in the last 6 months, so it's nothing major.

It would be a very slim chance of that happening on the first charge tho, but ask yourself this : Would you rather wait for a green led and then use the phone ... or do you want to stare at an orange led all day and finally write a post about how you think that your phone is not charging properly?

EDIT : oops, didn't see your other questions.

I wouldn't use the phone too much while charging.  When fully stressed, the CPU is perfectly capable of draining the battery faster than the charger can put juice into it.  So your battery could be charging and then briefly discharging several times, possibly shortening the overall lifespan.  There's no definite proof of this, but it never hurts to be a bit careful.

I prefer to start calibration with an empty battery.  Every time I did it from a near-full battery, it didn't seem to work for me.  Maybe a coincidence, but I've done the last 4 calibrations this way and judging by my standby times they seem to have been very successful.

Theoretically a charge should take no longer than 3 hours.  The difference between phone on and phone off is minimal tho.  it'll only be a matter of minutes.

As for the backup app, I'm afraid that's Sakai's territory.  He has described backup apps in his guide to a factory reset. 
I have my phone set up to use Google contacts instead of storing them on the phone or SIM, so if something goes wrong I can just do a factory reset, have them restored from the Google cloud and have the entire phone all set up again in an hour.  The only thing I lose is my sms messages, but IMO sms is sooo 20th century to begin with.  I barely ever use it. 

I tried this the other day but it made no difference 

So I've just tried it again and we'll see 

Incidentally, I have had my phone for just over a fortnight weeks and I have minimal use. I am not synched with friend streams, etc.

Actually (there's probably another topic about this somewhere, I'll have a look in a bit) ... when I look to see what's been draining the battery - what is the difference between Android and Android OS 

I really wanted an Android but I'm starting to wonder: if you have a phone that can do everything, what is the point of having said phone when doing everything kills it? 

No idea on the HD's battery life.  However I do know that calibration doesn't work on that one.  I suggested it to a few HD owners and none of them noticed any improvement.

You mean it turns green right away?  That means that the battery really is full.  Maybe they updated the firmware slightly.  Would make sense, seeing as they apparently got it right with the HD and the Z. 
What's the first 4 digits of the serial number BTW? 

That's pretty normal for a new phone.  After 2 weeks the battery should reach its full potential and you'll (probably) start using it less anyway.  So give it some time.  It'll turn out just fine.