I sent an email to Panasonic about the subject of cycle life vs depth of discharge after reading this and the reply came back including: "A more shallow discharge will yield a greater number of cycles." The person who replied does not, however, have any specific data for this including whether it follows a linear or non- linear graph for their cells. I've since emailed them again to ask for this information to be obtained but in light of the post in conjunction with what I've so far heard from Panasonic, I'll be changing my usage and following that advise, trying not to let the battery discharge much before recharging it.
With regards to whether using the bike until the battery is completely flat gives the same result as a refresh, no it won't. The reason why is that the charger's refresh function is especially designed to discharge the battery at an ideal (relatively low and slow) rate. Using the bike (even on econo) will result in much higher current draws and a very different discharge profile. The bikes own electronics may also cut-out the battery at a different voltage to what the refresh allows it to go down to (although neither allow it to dischage totally). The reply from Panasonic reccomended it never be allowed to fall below 1.0 V per cell and the website pdfs recommend a minimum of 1.2 V/cell where large numbers of cells are connected in series as on the Twist battery.
As long as you've travelled some distance on the bike (so the battery is at least partially discharged), there should be no concerns about recharging it. This is because the chargers that come with Twists are of an intelligent design to prevent over-charging and they'll switch off (in practice the red light flashes) at the right time. According to AtoB magazine, there were some problems with earlier chargers cutting off to soon and Giant arranged for users with such chargers to have them fixed or replaced.
If you've dropped the old battery, who knows what damage may have been done. The manual I have refers owners of damaged batteries to the dealer to get the battery inspected before any further use but if your LEDs no longer work then there's clearly been some level of damage. It's not for me to recommend you take the 2 year old pack apart to inspect it and effect a repair (especially given all the warnings against this on the battery and in manuals due to possible short circuits and fire etc).
The workshop service manual for the Twist lists A271GE0001A9 as the part no for the LFREE TWIST B/P COVER SET (B/P meaning battery pack). I doubt whether Giant UK will sell you just a cover set for the battery at a reasonable price but you have nothing to lose by asking, especially if the housing cracks/LED probs can't be repaired with glue and solder etc On the other hand if the old pack performance is poor, then you may not wish to spend anything on it (even though the cells could eventually be replaced at a much lower cost than a new battery).