Is Parse the best and easiest to manage backend for user accounts, IAP tracking, custom push, analytics and user data sets?

Parse is indeed one of the best for user accounts, IAP tracking, custom push, analytics and user data sets.
You can watch this video http://www.youtube.com/watch?v=E_0llIdtYNA on Youtube for some basic understanding of the Parse platform.

Indeed it is. Notable competitors were Stackmob, Buddy, wheras Stackmob was acquired by PayPal and subsequently shutdown (https://gigaom.com/2014/02/12/bye-bye-stackmob/) , whereas Buddy is still in the field with $3.6M of funding.

Looking at these competitors, they pale in comparison with Parse, which bascially has been given unlimited resources through the $80M acquisition by Facebook. This manifests in the fact that Parse has decreased its pricing vastly, because they are more looking to build an ecosystem of apps instead of making money. That's the advantage of using Parse over competitors.

Having used Parse for over 8 apps now, I can say that it only takes 1 hour to understand the documentation of one platform, however, there are some things that were not solved well with Parse.

Firstly, you can only query for 1,000 results maximum. If you want more results, you will need to run the query multiple times or you will need to make a work around.

Secondly, you cannot query for GeoPoints with in an inner query. That means, you can't put a query that queries all users in a certain area into another query and use the matchesQuery("objectId", query) command for instance.

These two quirks I don't understand why they are not fixed, but apart from that Parse is working really well and enables startups to set up their backend really, really fast. I've built messaging apps with a backend within 24h with Parse.

Yes, Parse is undoubtedly the easiest, especially considering the vast array of functionalities and options offered.