Using luks manager app for creating file based containers for encryption, is there any chance that unencrypted data appears in crash dumps etc?
With full device encryption, unencrypted fragments should be available in volatile RAM only – which means an attacker needs physical access to the running system. There's no such thing as 100% security, but I'd say that's as close as you can get, when combining it with a good lock mechanism (best encryption is useless if you don't lock your device and an attacker can get physical access).

Als for LUKS, I'd recommend checking with their project site, which contains a bunch of information. A raw scan (I don't use LUKS myself) even revealed information on how to use LUKS to fully encrypt partitions on the Android device. The LUKS team will also be the best address for technical details.