(1) If I purchase this IPOD will I be able to download Apps without any problems?
Yes, AS LONG AS you are connected to a working Wi-Fi network that is connected to the Internet.
(2) Is there a way to transfer these Apps from my computer to the IPOD?
Yes. See here: Syncing and arranging apps from the App Store
(3) Are there any good Apps for keeping track of foods (calorie content), weight, etc.?
Yes. Search the App Store or do some research via Google regarding google calorie tracking apps.
(4) Can I check my hotmail account for emails in my car or anywhere I may be?
You can only check for email when your iPod is connected to a working Wi-Fi network. It does not use a cellular data connection like an iPhone or 3G/4G iPad can.
(5) I know many Apps are free; however, what are the prices for different music?
Songs prices vary. Any where from free to a couple of dollars. You'll have to just look around the Music Store to get a better feel for the pricing model.
(6) What kind of accessories would anyone recommend for this IPOD?
Definitely a case of some sort that will protect it from scratches or further damage if dropped. That's about all I will offer though.
Any other information that might be helpful to me would be appreciated?
8 GB isn't that much storage space especially after you consider that some of that is taken up by iOS and take into consideration how storage capacity is reported. You'll only have about roughly 6.5 GB of free space to use. So if possible, I would purchase the version with the next highest capacity at 32 GB.