I just finished reading the 59 pages of this thread to be able to resolve my problems. The first one seems to be a known XDK bug, but I will still explain it here.
My bug seems to be similar to this one : https_://crosswalk-project.org/jira/browse/XWALK-2655 (delete "_" as I'm not able to post links)
My game runs perfectly while previewing over wifi on Chrome for Android, on my two devices : Samsung Galaxy Young GT-S6310N and Samsung Galaxy Tab3.
In the emulator of XDK, it works fine.
When exporting with Crosswalk for Android, then playing the APK on the devices :
1) On the tablet, I can see the title screen, then it crashes most of the time. I'm back on the menu screen of the tablet, then if I check the running apps, I can still see my app running there. When I click on it, I'm back to the C2's loading screen, which sometimes freezes, or it either crashes the game again, or succeed to launch the game.
2) On the mobile phone it's the same, except that I'm not sure the game started even once. It crashes nearly always.
I tried XDK beta and stable, it behave the same way.
I send the exact same build to a friend which tried it on a Samsung Galaxy S3 mini, and up to now, he has no problem playing the game. Everything runs perfectly.
The project is quite big (around 9000 event for now)
I read some people saying that they have problems with the sounds. I didn't test to delete the sounds yet, but I have a music (placed in the "sound" folder, not "music", because I want it to preload) during the title screen, and the sound plays on both devices, so it's probably not related to sounds.
I also read that there was problems with the blacklist of webGL on some devices, including some devices from Samsung. I did the following test : created a new project that just displays the name of the renderer, and it returns "webgl". Don't know if it helps.
I'm also facing another bug, which seem to be related to webStorage : When I activate the loading of webStorage (loading of about 60 number global variables on my title screen) and runs the game on my tablet, it's behaving correctly on preview over wifi running in Chrome for Android (IIRC, need to retest, but at least in Construct preview it works fine), but here, even in Intel XDK's emulator, I'm experiencing another problem. The title screen works ok, but when the game launches, some object simply doesn't appear. On one level I had all my characters diappearing, on another I had the background disappearing. When I turned off all loading of webstorage, this bug was resolved... But I will need webstorage to publish my game...
One last note : I'm not a programmer at all, and I don't know how to display the error message in XDK, or when trying on the device. Could someone explain, so I can eventually give additional informations?