@72:
To answer your questions:
1. Short answer, yes. Long answer, only if you don't have an Apple developer account. If you do, apps expire after a year but even if you didn't, you could Jailbreak an iOS device to get the functionality to automatically sign apps so you don't have to.
2. No, there's no limit.
3. I've only got Sixth Sense and at the time of writing, I'm working out a way to get the IPA from an app, assuming everything goes to plan. I'll upload that on Dropbox if it works so keep an ear out for that.
@73:
Something else people might get confused about is the password generation. You only have to do this if you have 2-Factor Authentication enabled for your AppleID. Otherwise, you can use your normal AppleID password.
@74:
There is technically a way to do this. You'll need to jailbreak your chosen iOS device so if you're not comfortable or don't want to do that then that's also out of the question.
Hopefully you can get another cable soon.
And if anyone's asking about the shady/grey areas about jailbreaking, here's a video that should answer all of your questions regarding if this process is illegal, if this voids your device warranty, ETC.
https://www.youtube.com/watch?v=1Ry3D-EuwMU
Hope that helps everyone
Edit: Can't find anything that'll let me get an IPA from an app, asking a more-experienced friend to see if they know anything. Searching didn't give me anything useful. If anyone of you know how to do this, don't hesitate to let me know.