You can use FM, AM, QAM, or other multi-bit modulation schemes to send that information, but you need to have the signal-to-noise ratio to demodulate it. WiFi actually goes up to QAM-1024 (10 bits per symbol) in the more recent specs. However, the SNR you need to decode that is perfectly is something like 35 DB, while recovering a signal that sends 1 bit at a time needs ~3 DB. A 35 DB SNR is very hard to reach unless the RF environment is quiet (basically impossible in an apartment building, for example), but 3 DB is easy.
Shannon's limit tells you about the total information capacity of a channel given its bandwidth and SNR. This is usually achieved by using deeper modulation than theoretical, and using error-correcting codes to recover the lost data.
Modulated signal could be expressed as sum of signals with different frequencies, but will it be registered by receiver as signal at these frequencies?
Suppose we send 1hz signal with length = 1 hour. In the middle we change amplitude of one wave to 1/2. Does recievers recieves mix of different frequencies?
The only signal that contains only 1 Hz and no other frequencies is a perfect 1 Hz sine wave. As soon as you start modulating the amplitudes away from that sine wave, you're introducing content at higher frequencies. You can use that higher frequency content to transmit information at more than 1 bit per second, but you're not exactly using the 1 Hz signal to transmit information.
SSB still makes other frequencies. Viewed on a waterfall, it's just half of AM, minus the carrier. Still occupies a range of frequencies, approx half of what AM does.
10 bits is at least plausible, but if you want to try to transmit .1 kbps with no frequency content over 1Hz, you're going to need the mother of all SNRs.
Suppose we have 1Hz signal, what stopping us from sending/receiving 10 or 100 bits of info every second by modulationg amplitude of signal?