Multiband LNA Design
1) what are the challenges in designing amplifiers for high frequencies?

Lets split that question into 2 parts

------narrowband design

A narrowband design, with low phasenoise Local Oscillator, might have 100Hz bandwidth; NASA communicates with some satellites at such low bandwidths (low data rates); in a 50_ohm system at room temperature the noise floor will be 0.89 nanoVolts RMS * sqrt(bandwidth), and a 100Hz system (which will support approximately 100 bits per second data rate) has noise of 0.89nV * sqrt(100) or 0.89nV * 10 or 8.9 nanoVolts RMS noise floor. With Shannon limit being near 0dB SNR, the recoverable signal energy will also be 8.9 nanoVolts RMS signal.
To feed the signal into a quantizer/digitizer/ADC at 1voltRMS (2.828v PP) you will need a voltage gain near 300 Million, without oscillation.

Yet VDD distribution circuitry (providing power for each of perhaps 20 stages of gain or mixing or variable-gain (to provide adjustable gain to maintain near full-scale ADC loading)) will have resonances, and you must prevent the VDD wiring being a sneak feedback path.

You also need to select a precise small range of frequencies; that requires you learn about phasenoise behaviors, because angular noise of Local Oscillators will mix with close_in and far_out "noise" (random and periodic), degrading the SNR; further, to select a small range of frequencies, you need sharp filters either by cavities or striplines or LC or active filters (usually with noise floor far above default 50 ohm floors of passive filters)

------broadband (DC --- light, 1MHz to 100GHZ) design

In broadband design, if you need FLAT frequency response, then any resonances (unless properly dampened) will be a problem; and there are several methods to cause resonances

a) modes of energy storage in the cavities of any shielding structures

b) inductance + capacitance energy storage

c) stripline energy: power strips, signal_in strips, signal_out strips, GND 
      strips (2milliMeters of metal causes 2mm of delay and also stores energy)

d) the VDD distribution "tree"

Also broadband design is very vulnerable to coupling between input and output, yet the tuned circuits are not permitted to reject unwished energy.

2) above what frequency does "normal opamp" no longer work?

There are at least three tradeoffs here

a) a diffpair with emitter-follower (the Cherry-Hopper circuit) may be used at quite high frequencies, because the total phase shift is very small

b) inductances become a big problem, partly because GND becomes an uncontrolled node

c) 10pF capacitance at 1 volt RMS at 10GHz requires what power?

Power = F * C * Vrms*2 = 10^10 Hertz * 10^-11 Farad * 1voltRMS^2 = 0.1 watt

Thus an opamp driving 10pF at 10GHz at 1 volt RMS must provide 100 milliWatts to the load. 

3) the ART of LNA design : distortion, Zin, Zout, Noise Floor, phase shifts that upset data eyes, VDD filtering, ESD survival, instability (oscillation) for various Zsource or Zload

4) noise matching: because signal energy becomes so precious (gain becomes so difficult to achieve), we seek conjugate matches between stages;

5) why are only a few large transistors used: we cannot use the standard OPAMP because the UGBW may be only 1,000MHz or 2,000MHz; we accept we cannot use large ratios of feedback resistors to achieve precise gain because parasitic C across the resistors lead to capacitive-division setting the gain, not the resistor ratios; we use a few large transistors, operating at HIGH CURRENTS to provide HIGH TRANSCONDUCTANCE, perhaps with emitter resistors to linearize the stage gain and push IP2 and IP3 up to high intercept levels for satisfactory distortion; for channelized communications such as cellphones, the IP3 behavior is key