Q: iMac (10.8.2 OS) loses IP address to HP printer

I have three issues that I suspect are related:

1. My iMac at home loses its Internet connection on a regular basis. Often, hitting refresh a few times in Safari makes the Mac remember it's connected to the Internet. I have both a wired and wireless connection available, but I disconnected the ethernet cable because I want to share my iTunes collection over the WiFi with iOS devices on the network. Even with both the ethernet cable and WiFi connected, the iMac would still lose its Internet connection on a regular basis.

2. Often, when I'm connected to my iTunes library from an iPhone or iPad, iTunes on the iOS device stops responding and seems to lose access to the iTunes library on the iMac. In keeping with the iMac losing its Internet connection, I'm guessing it's also losing its network connection in general, thus disrupting the connection between the iMac and the iOS device.

3. I had a problem with an HP OfficeJet 7410 printer, which allows for wireless printing, where the printer's IP address kept changing. I thought this was a problem with the printer. So, yesterday, I installed an HP OfficeJet Pro 8600 printer, which also allows for wireless printing. The HP printer found an available IP address, and then a short while later the iMac complained another device was using the same IP address it was using. This would suggest that the 7410 printer's IP address problem was somehow being introduced by the iMac. I didn't have any problems with the printer before I bought the iMac last year. Introducing the new HP printer has helped me establish that something funny going on with the iMac is really at the root of my HP printer IP address problems. Either the HP printer is attempting to commandeer the IP address that the iMac is using, and the Mac would give up its IP address somehow. Or, the iMac is giving up its IP address and then HP printer is taking it, and then the iMac remembers it was using that same IP address and then it introduces the IP address conflict. If the iMac relinquishes its IP address and finds another device trying to use the same IP address, it seems natural to me that the IP should go get a new IP address instead of fussing about the lost IP address and failing to work.

Note that I have two Windows 7 PCs, an Xbox, iPhone and iPad and never have Internet connectivity issues with my home network. I have a Netgear WNDR3700 wireless router. I just updated the firmware.

It would seem that if I can assign a fixed IP address for my iMac and somehow set my router to not allow another device to use that IP address, then I should stop having problems with the IP address conflict. So, any advice on how to go about doing that would be appreciated.

As for why the iMac loses its Internet connection, I'm not convinced this is all about the Mac losing its IP address to another device on the network, but I suppose that's possible.

Any advice on these points would be appreciated.

Thanks.