Yo man, I'm hoping your english is better than your french but when you use a Floyd Rose tremolo you gotta get it parallel with your guitar top otherwise it wont stay in tune, get it ?
I'd recommand you to slightly upgrade your string gauge to something bigger on your E string as you want it to be a C#. Depending on your guitar scale (but admitting it is a 25,5" as you got a floyd rose) you should use a string set more or less 0.10-0.56/0.60. Any further question ? Usually as I said at the beggining it is the kind of issues lots of people got because their tremelo is not set up right.
Btw ofc if you switch bitween tunings that is the kind of thing which is gonna be a permanent issue with staying in tune... As the tension on the tremolo is gonna be always different so all the strings are gonna be out of tune... There is an accessory called D-Tuna which has been concepted to swtich from E to D tuning on the E string of a Floyd Rose Tremolo. But as far as I've tried it it only works from E to D and not lower tunings (very hard to stay in tune)
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