At the end of the day, you can compile and run anything on your machine. This is just regulating distribution. Given the specific breaches at hand by Facebook and Google, a balance seems to have been found (acceptable to most users) between freedom and security.
It's free to get one though, but it only lasts for a week or so. You can pay to become a developer and I think you get one that lasts a year instead.
I agree that Google Play Services is not competition friendly, but that is a different topic.
Iff you have a Mac. And even then, you need to recompile it every week.
I'd prefer something else for my personal toy applications so I don't even need to bother with this, but it's not a huge deal to me.
The advantage of the Free Profile is that (afaik) it can't be revoked or censored. Disadvantage is 7 day lifespan.
Not really. You have to pay the ransom^W^W$100 for a developer account every year.
The installer is a piece of software made by Apple, to install things that meet certain criteria(ie signed packages). It's not that you can't technically "install" other things, but there doesn't exist a mechanism to do so.