Your comments

well..after some monthes and lot of tests seems (maybe) I have understand why it not wakes-up me with music but with the Phone's ringtone;
seems..i seems that doesn't overwork upon all lockscreen togheter all
battery savers I could try,
for example : juice defender or the own battery saver .
If I disable these 2 features, leaving the lock screen ON by hands or in automatic, juice defender disabled at all and the battery saver under Settings-->Power supply-->Energy Saver, it works very WELL..lovely and with love music radio starts as I would dream and my morning wake-up is the best I can.
This is what I have notice after lot of tests .
I'm on Android Revolution HD 31.6 by mike1986 (custom ROM with Android 4.3)...
fuc****** kitkat ;-)...I don't like bugged advertising's Android versions.
Best Regards ....yaris68
Happy New Year to you too;
ok..answers in order :
1 and 2. This happen not at first time I set a new alarm but the second time (the second day of it);
    the first time (my alarm has been set every day at 06:50AM) it works good, not the other times.
3.           I use HSDPA  stream for all my things by my phone need to use home WIFI;
              WIFI on my HTC ONE is always disabled, as it is very lower than HSDPA I can use.
This probles has happen all times as with stock ROM as with other ROMs with ANDROID versions
from 4.2.2 to my actual 4.3,
just once or twice..with some version of XiiaLive all were good.
The main reason I bought XiiaLive was to wake-up in the morning with music and not like now with the normal ringtone.
In the setting panel I can set  fade and snooze lenght as I like but nothing change, after the first time (when it works good)  the problem restart and I have no idea why.
Actually I have ANDROID v4.3 not stock ROM.

Best regards .................. yaris68