I've probably bought around $2000 total from Newegg, from monitors, every piece of hardware that goes in the case...
Processing
They usually process the order within 24 hours, and a fair amount of time the same day. Although I've had 'em take up to three days before, but that was a holiday weekend, so, yeah...
Timing
The cheapest shipping on Newegg (in general) is the "UPS 3-day Guarantee" - so the longest the majority will say is just that, three days... It all depends on where you're at relative to UPS's shipping routes... I always get my stuff in three days even though Tucson is relatively close to the warehouse in California - however if you lived in Phoenix...you'd almost always get it in two (since UPS routes through it).
And likewise as to what other's said...it could come from a different warehouse all together.
Damage
Everything I have purchased from Newegg has been extremely well packaged
when it is a smaller item - graphics card, memory, etc. They put them in rather large boxes with plenty of protection - UPS can throw it around if they want. However, when it's a big item such as a computer case or monitor...they tend to ship it in the original box, and that is where the trouble comes in. I know a few people who've gotten a case dinged up thanks to UPS (and FedEx) along the way...since they're not padded all too great. It'd be interesting to see how they fare going across the ocean
Also, as b1gapl mentioned - they don't ship internationally - I know they were attempting to expand into Canada, but even that has not happened yet. From their FAQ:
Q: Does Newegg.com ship internationally?
A: Newegg.com does not currently ship internationally; we only deliver to locations within the United States and to Puerto Rico.
Lots of fun...