Brief introduction to wireless communication and communication terminologies
Well, these are very fundamental questions, and I think they are written in any good book. But maybe it's hard to extract the exact information from them, which you ask for. So, let me briefly answer:

In wireless, the channel is usually modelled as a FIR filter with impulse response $h(\tau)$. But, this channel might change over time (due to e.g. mobility), to make it a time-variant impulse response $h(t,\tau)$. Moreover, the channel is often modeled as a tapped delay line, $h(t,\tau)=\sum_ia_i(t)\delta(\tau-\tau_i(t))$ where $a_i(t)$ are time-varying gains of the taps and $\tau_i(t)$ are the time-varying delays of the taps. The fact that $a_i(t)$ has complex values does not make it Rayleigh fading. Rayleigh fading describes the temporal distribution of $a_i(t)$. If over a long time range the distribution of each path gain is a Gaussian, it becomes Rayleigh fading. The doppler spread of the Rayleigh fading describes how quickly the value $a_i(t)$ changes over time. In the special case of block-fading $a_i(t)$ is a constant (the channel remains static) for the whole transmission. Then, when a new transmission starts, a new channel is generated. Then, the realizations $a_i$ follow a Gaussian, to make it block Rayleigh fading.

A multipath channel corresponds to the tapped-delay line model. Have a look at one of my articles about multipath propagation, maybe it helps. The number of inputs and outputs depends on the number of TX and RX antennas of your system (talking about MIMO systems here) or the number of users. For single-antenna systems there is just one input and one output.

The input to the physical channel is analog, if you model it as a tapped delay lines. However, you can assume transmission in passband, then all signals are real. Or, you can do an equivalent analysis in baseband, where all signals are complex but the math is easier to treat. For the description of transition from baseband to passband, you can look at another article of mine.
Though, there are other channel models such as BSC or BEC, though these are not used to model the transmission of an analog signal over the wireless physical channel, but abstract away from that.

Modulation is performed after encoding ;-). Modulation means to generate a signal which is adapted to the channel, a a function of the transmit bits. It can e.g. include mapping the bits to complex QAM constellation points.

Encoding takes your bits you want to transmit (the payload) and adds redundancy via a channel code. This way, if at the receiver side, one bit is lost, it can be recovered by appropriate decoding.