Oh thank jeebus! I thought I was the only person who had this problem. I've been searching all night trying to find a solution to the problem.
I guess you can tell that I am experiencing the exact same symptoms with the search as you are. I wish I had a definitive answer for you on how to solve this.
That said, the Enter key did work twice tonight for me when I fiddled with settings (e.g. the regional settings), but immediately went back to crashing right after.
I get this in my event log when SearchUI crashes (and, it does indeed crash when you hit Enter on specific items such as folders... hence the pause):
Now, certain items, like the Windows Store, Calculator, and Settings (these are the only ones I've tried) are working with the "Enter" key.
Faulting application name: SearchUI.exe, version: 10.0.10240.16515, time stamp: 0x55fa5578
Faulting module name: CortanaApi.dll, version: 0.0.0.0, time stamp: 0x55fa5354
Exception code: 0xc0000409
Fault offset: 0x000000000013e739
Faulting process ID: 0x25a8
Faulting application start time: 0x01d11c51f2a62d24
Faulting application path: C:\Windows\SystemApps\Microsoft.Windows.Cortana_cw5n1h2txyewy\SearchUI.exe
Faulting module path: C:\Windows\SystemApps\Microsoft.Windows.Cortana_cw5n1h2txyewy\CortanaApi.dll
Report ID: 95204738-8ae8-4b58-b7d8-a2d2abf52bee
Faulting package full name: Microsoft.Windows.Cortana_18.104.22.168_neutral_neutral_cw5n1h2txyewy
Faulting package-relative application ID: CortanaUI
I figure something got broken via an update. I hope they fix this fast, I rely on this way too much.