Funny, I went from an iPhone 4 to a DX.
Moving from the iPhone to an Android device is definitely a change. You might have been better off moving to an HTC device with sense. They seem to have a bit more polish and iPhone like features.
I had the same Airport issues as you. Luckily for me I have two routers in the house so I switched to my Linksys, and haven't had any other problems. WiFi outside the house has been fine.
If you are having reception issues at work then you definitely need to switch carriers. Simple as that.
My typical day consists of a few telephone calls that probably add up to less than 30 minutes. I have Gmail and an Exchange account that poll all day. I do some minor surfing and texting. All told after 10 hours I typically have 70%-80% battery left. That's better than my iPhone 3GS and in the same area as the iPhone 4. Mind you I have the display set to a low level. The display backlight can use a lot of power.
The vibrate function can be remedied with a simple widget or just turning the ringer volume up one notch from silent.
One of the primary reasons I left the iPhone was the poor notification system. I typically leave my phone at my desk (where I get a signal) when I need to work in other parts of the building that have zero reception (15 foot thick concrete walls prevent any wireless reception). When I get back to my desk I have no way of knowing if I received a call, email, text, etc. unless I wake the iPhone. Then I may need to wade through multiple apps to check everything. On the DX I can just look for a flashing indicator. If that is flashing then I can just wake the phone and pull down the notifications to check everything. That's golden for me.
Task management is easier on the DX as well with widgets. I no longer have to switch around to several apps when I can have everything on the desktop with widgets. It is so much simpler.
The iPhone is still a very good device. The camera and video is much better on the iPhone 4 than the DX. The system wide cut and paste is light years ahead of the poorly integrated mess on Android. The best part is that you can get a free case for the iPhone.
Sorry I couldn't resist. Best of luck.