Can I use a crystal oscillator (not resonator) output for this pin? The datasheet doesn't directly mention if it can be used with an oscillator, so I thought that maybe it requires some other kind of a signal.
The requirements for CLKIN are:
any frequency from 10 to 100 MHz (datasheet section 4.1.2)
Low/high levels that match the requirements in Table 6:
When powered with 3.3 V, this corresponds to a low voltage of up to 0.99 V and a high voltage of at least 2.31 V. This seems to match up with the LVCMOS standard listed in the figure you show under question 2.
You are correct that you'd need an oscillator, not just a bare crystal or resonator. It doesn't necessarily need to be a quartz crystal oscillator; for example it could be a MEMS oscillator instead.
If your oscillator has an LVCMOS output that swings over the same range as your Si5351C supply voltage (e.g. both are 3.3 V), then this should work. If you aren't sure, you may want to edit your question to identify the oscillator you wish to use.
But I'm not sure what the cylindrical shape means - does it represent a 50 Ohm resistor? If so, why is there another resistor in series to this one?
The cylinder represents a transmission line with controlled impedance, which is important for high-speed signals to avoid reflections and other signal integrity issues. This could be a PCB stripline/microstrip/coplanar waveguide, or it could represent a 50-ohm coaxial cable. The series resistor is a series impedance matching resistor that matches the driver to the transmission line. The exact value would depend on the output impedance of the oscillator you've chosen.
It's not clear why there's no termination resistor on the Si5351C end. I don't think there's a 50 ohm termination onboard the chip according to Table 4, since the max current drawn through CLKIN is 10 microamperes.