In case of using a Doppler radar, do we have to use IQ demodulation to find the direction of a target?
Radar designer here: It sounds like you’re talking about  pulse-Doppler (PD) radar systems. For PD radars, the process is essentially as you described:


Generate a waveform (typically at IF) and then convert to RF
Transmit the waveform at RF
Receive the waveform at RF, and eventually mix it down to IF. 
Apply IQ demodulation (for digital receivers a Hilbert transformer is typically used but that’s not an important detail). In this step, the received signal is added with a version that is 90 degrees out of phase with itself multiplied by the square root of -1, or the imaginary number. In general, you’ll have the generic signal s(t) = I(t) +jQ(t), where j is the symbol for the imaginary number. You can accomplish IQ demodulation in analog hardware, or you can use a digital receiver to accomplish it as well when you sample (via a Hilbert transform)
Collect the individual pulses and “stack” them in an array
Perform pulse compression and Doppler processing. Doppler processing is accomplished by computing the DFT across each pulse.


Since each waveform has phase which is recoverable with IQ data, the cross pulse DFT basically allows you to see the rate of change of that phase information, which is naturally the Doppler frequency. By being complex, yes you can tell whether a target has a negative or positive velocity, which is naturally very useful and pretty crucial for most tracking radars.

As for your question about needing to modulate the waveform: if by modulation you mean something other than a pure sinusoid, yes generally that’s a good idea for pulsed Doppler radars, as you’ll need good pulse compression. LFMs (linear frequency modulated) signals are a popular choice due to their nice properties, though other modulation schemes exist (NLFM, PSK, FSK, etc). If you just use a pure sinusoid, you effectively get no pulse compression, and you’ll have a pretty poor estimate of where targets may be, and the performance would be awful if you have several closely spaced targets.