In real shematic for AM simple receiver, there is no ampification
bewteen the antenna (and the tuning LC circuit) and the diode. So how
the diode manage to half-rectifies correctly in real operating mode
when the signal is weak and high frequencies, which is the case of
real
radio signals.

You'll find that in reality something your simulator won't take into
account that its preferable to transmit at higher frequencies because
reception is better as the 1/f flicker noise is reduced to lower
values. Thats just 1 of the several reasons why frequency multipliers
are used in transmitters and downconverters in receivers.
I use Ansoft Simplorer mainly. Any other simulators recommended ?
Thanks in advance and best regards,