Question 1: How to send EXE to WinIoT device and run it.
As on WinIoT 10 Core there is no shell, there is also no way to run a program as you are used to it on a desktop machine. First how to bring it to the device. You can either connect your device to the same network as your development device is. This is described on the following side: http://ms-iot.github.io/content/en-US/win10/samples/HelloWorld.htm . An other way would be to crate a Application Package and upload the application to your device using the remote interface. This is kind of a website, that let you manage your device. More information on that you get here. On the Remote Interface you can also start and stop programs as well as define a default App, that gets started when the devices boots. Follow the links in the previous linked developer page for more information.
Question 2: Run several program at the same time
WinIoT 10 Core allows only one application running the same time. You can compare this concept with Android or IOS devices. You still can run background task (command line applications or services) the same time.
Question 3: Is there a file explorer?
No, there is no file explorer. We recommend to use the remote interface to run and terminate applications as mentioned above.