If the receiver uses mixing (like a superhet) it is trivial to detect radiation from the receiver. This was widespread 70 years ago (https://en.wikipedia.org/wiki/Operation_RAFTER) and has almost definitely been expanded to modern radio by today's spy agencies.

There are commercial receivers that can be placed near the side of the road to measure the popularity of broadcast FM stations by measuring LO leakage. Definitely not limited to TLAs.

> A old times radio receiver, it cannot be detected? Or can it

Old times radio receivers are low power transmitters. Their local oscillators leak out of the antenna enthusiastically.

The physics hasn't changed. There is far less leakage in modern receivers, but our detectors are way more sensitive as well. And if you're a nation-state and free to fly drones over rooftops looking.... yeah, don't believe anyone that claims they can operate anything involving electromagnetic energy without risk of detection.

Yes, you can locate even passive antennas by broadcasting a wide-band signal and looking at the reflected spectrum. It's way easier if you know the frequency that the antenna is tuned to.