OFDM RF signal waveform
(1) Yes, if the technology permits it for the power handling requirements of the design, the strategy is to filter as much as possible immediately at the front-end of the receiver prior to the LNA. The primary reason is jamming from stronger signals. Depending on receiver topology used we would be concerned with 2nd and 3rd order intermodulation products and receiver phase noise that can be induced on out of band signals if significantly stronger all creating noise in band that would limit our receiver sensitivity. 

FBAR technology is an excellent choice for front-end filters combining low loss and exceptional rejection. I have used FBAR filters in the design of femtocell cellular base-stations where the constraint was to receive the entire band (in this case it was a duplexer so would be used to receive 1850-1910 MHz and transmit 1930-1990 MHz --- notice the 20 MHz spacing between these two bands that this technology was able to provide exceptional isolation up at 2 GHz). We use the low loss band-selecting filter due to linearity/intermodulation concerns with the LNA, however with FBAR one must also be very careful with inter-modulation effects especially when using these filters in multi-carrier designs. Here is a good online article with more details about FBAR and other filtering considerations. 

http://www.linleygroup.com/mpr/article.php?id=11440

(2) The distortion you are referring to is concern with frequency offset. Frequency offset will always exist since the typical transmitter/receiver set do not use a shared clock. The two dominant sources of frequency offset are the offset of the clocks themselves and additional offsets under dynamic conditions due to Doppler.  The relevant standards will specify the maximum allowable clock offset for the design, but &lt; 5 KHz is a reasonable maximum possible frequency offset at 2 GHz for lower cost technologies (this is driven by the ppm specification for the master oscillator used).  If I calculated correctly the Doppler at this frequency when the transmitter and receiver are moving apart from each other at 60 mph would only be 179 Hz. The combination of both of these numbers will be well within the passband of whatever front-end filter is used, as no such filter would have a brick-wall response. 

(3) I think you are confusing the carrier (2 GHz) with the bandwidth at that carrier (20 MHz). The actual carrier frequency is irrelevant to how much data we can transmit (without consideration to path loss effects on signal power for the SNR component of capacity).  The theoretical maximum symbol rate is given by the Shannon-Hartley equation for maximum channel capacity which accounts for both SNR and BW: 

$$C = B \log_2(1+ SNR)$$

Where: 

C is the maximum capacity in B/sec
B is the bandwidth of the channel is Hz
SNR is the signal to noise power ratio (not in dB but ratio of power)

Note MIMO technologies exceed this by utilizing multipath to send multiple "channels" simultaneously. 

For more info on Shannon-Hartley equation see:  

https://www.gaussianwaves.com/2008/04/channel-capacity/