Can long-range radio waves from an RTV tower penetrate thin plastic composite material next to its source?
covered with antennas and aesthetically it looks unpleasant and way too much utilitarian. 


… I heartily disagree, but  that's just a matter of taste.


  My problem is that I absolutely have no idea what these devices are. Are those receivers or transmitters?


These things are antennas; some are used for receiving, others for transmitting, most for both.


The red longish ones look like common 2G/3G/4G cellular antennas.
The smaller rectangular antennas might be the same
The large dishes on the left of the tower pointing into roughly the same direction are probably satellite dishes pointed at geostationary satellites.
The "drum-like" round ones are high-directivity microwave antennas for stationary point-to-point links. They provide such things like giving cell towers elsewhere an uplink to the cell provider's backbone, or directly attaching factories to company networks, or are the link used by a radio station to bring the radio signal to the broadcasting tower. They are also dish antennas, but in a protective housing with a relatively RF-transparent shield against weather in front.


Then there's things I can't assess:


There's the big, dark-gray "sphere" on the lowest level. That's probably a radom, i.e. a housing for a movable antenna. The fact that it's dark might indicate it's actually usually used in naval or military applications. It might be tracking a satellite, or ships on the sea, or troops on the move. 
The second level has these gigantic "cut-off tubes"; I've never seen something like this; these might be military high-bandwidth antennas, but that's pure speculation.



  We want to envelop the tower's central body, beneath the upper gondola and part of its lower gondola with organic, deconstructivistic "curtain facade" made out of highly perforated (ca. 60%) approximately 5 mm thick lightweight plastic composite material panels, to visually "hide" those antennas behind, and to give the tower a brand new vibrant composition mixed with LED lights for night light shows, which will make it very eye-catchy from Zagreb and all surrounding cities.


First of all: you're asking the wrong folks. These platforms have been rented out to companies operating these antenna systems, and all hinges on them agreeing to your plans – it's very unlikely a touristic attraction would ever generate as much revenue as the infrastructure is worth here. If at all possible, you need to have goodwill of whoever owns these platforms they rent out, and political support from above. The operators have rented the platform with guarantees about unhindered line of sight, with power reliability levels, and with a guarantee that the antennas are easy to access for maintenance, and access to the antennas is strictly regulated.

 

Then: I like the idea, aesthetically :) ! 

So, plastic will absorb RF, and that will be hard to sell to the people using these antennas. However, that effect scales with the percentage of that plastic that's actually holes, and there's worse and better plastics, so there's potential for compromise. However, expect things to become more expensive than thought.

Then: "Composite" is a bit too vague. There mustn't be any metal in front of these antennas. That rules out the possibility of putting LEDs directly in front of them. 

Apropos in front: Human workers mustn't accidentally happen to end up in the beams of these dishes. That's microwave. In your microwave oven, you use that to cook soup.

So, all in all, I don't think that putting something in front of these antennas is actually feasible, and especially politically much less feasible then technologically. I still think your concept could work – just exclude the platforms from the enclosing, and maybe work with conformal light projection on these surfaces. The operators don't get a word about which pictures are projected onto their antennas :)