Can I make iPhone apps just for myself?

You'll need a dev subscription to digitally sign it because unlike Android, iOS will only accept apps that are verified by Apple, otherwise you will get an install error.

Same goes with music and videos, the one reason I refuse to get an iphone. The only way around this is to "jailbreak" your iOS device, the equivalent of rooting an Android device which will most likely void your warranty.

I believe you need the developer subscription to install it on your iPhone, but you definitely do not need to put it on the app store in order to install it. Note that I'm not really sure, as I have the subscription and never tried installing a home-built app on the phone prior to subscribing.

You could build it in HTML & Ajax and then just install the site as a home screen icon. iPhones allow offline browsing so no reason why it won't work - don't even need the development kit!

You could develop it and never ask for approval so it doesn't go into the store.