I'm typing in

/set sv_pure 1
/set sv_official 1
/map cqb_sample

I've also tried

/set sv_pure 0
/set sv_official 0
/devmap cqb_sample

Any suggestions?

I've been able to connect and play online.

is not needed, all you need is

BUT:
the system behind sv_official checks ALL Pk3s et loads when you run your lokal server, so this includes pk3s in your etmain folder, any pk3 that doesn't ship with plain et (pak0.pk3 to pak2.pk3 + mp_bin.pk3) has to be removed

That did the trick, thanks Merlin!

Whenever I go to the "Host Server" menu and try to start a server, the game immediately crashes when I click start ... I've tried changing some settings but to no avail. Any ideas?

P.S.
This happens, for some maps, in TC:E too.

In TCE all I did was type

/set sv_pure 0

then

/map whatever_map_u_want


Now there seems to be lock in CQB. Cant play any other map but the sample map.

Does anyone know the secret to playing other 3rd Party Maps on CQB?

Yes. Crack the "/sv_official 1 checkloop" with a hexeditor. And don't forget to share it

this often happens when u got a lot of custom stuff (maps, sounds/weapons,...) i would suggest temporarily move all custom pk3's (yy_, zz_.. obj_..) to a seperate folder (eg. custom maps), this should let you start a server properly.
as for cqb its basically the same, make sure u dont have any non-official stuff in the folder (maybe dl'ed,.. by accident) and as merlin said, clean out ur etmain folder from 3rd-party pk3s as well.
optional (not needed but cant do any harm ): add this to the autoexec.cfg
set sv_pure 1
set sv_official 1

That worked, now I can host CQB games (haven't tried TC:E yet).
Thanks