With Windows 10 Microsoft introduced a new browser with a lot of new features never seen before in any existing browser (at least without possible plug-ins): for example, you can draw over the browsed page and possibly share it, you can save  a browsed page in the reading list without the need to add it in the favorites,  you can choose the reading view for better read (and  possibly print) the content of a web page. …

However I think that there are still something missing to make it the preferred browser and it will take some time to wait, … but the way is the right one 😉

For example it is not always easy to import favorites from other browsers and no synchronization (with the cloud) is maintained among different computers for the same (Microsoft) user [as it works for Internet Explorer].
P.S. (12/10/2015): the Inside Prerelease Build 10565, just released, should have introduced that syncing feature for both Favorites and Reading lists.

It is not easy to select another search engine (and possibly consider as the default one): only after visited at least once from Edgea a site with search engine (e.g. wikipedia, google), you will find it in the list of the available search engines!! It is quite strange … I hope it will change in future releases …
Moreover it is not clear how one can easely select the proper search engine to be used for a particular search (afterwards, after having added it in the previous list but not selected as the default one), without having the need to change every time the default one: for examp0le, in Internet Explorer this feature is available simply clicking near the address field).

Google searcher is not listed because I never browsed it in Edge

Google searcher is now listed after having visited http://www.google.com

It is not a case, in my understanding, that the Windows 10 Enterprise 2015 LTSB (for enterprise) do not (still?) have Edge as a browser and that, by design, the default administrator of a PC cannot run it (if you try, you’ll receive the error “Microsoft Edge can’t be opened using the Built-in Administrator account.  Sign in with a different account and try again”): if you really want it, you must do some changing in registry settings.

Edge not available for built-in administrator

Anyway note that the built in administrator does not even have the searcher be able to find out the IE browser and, if you want to launch it, you have to create a link (e.g. on the desktop or as a tile) directly to the program file (C:\Program Files\Internet Explorer\iexplore for 64bit or C:\Program Files(x86)\Internet Explorer\iexplore for 32bit).

In order to better manage the favorites in Edge, you can have a look at this tool: Manage Edge Favorites