The ropes I fix the bike with on the rack and the rack itself (although covered with a plastic layer (an old inner tube) make marks on the frame. I would like to avoid using extra pads, sponges or foams that always gather dust and dirt or fall off the correct place. Is there any special trusty method?
Pool noodles, cut lengthwise and held in place with gaffer tape (or hockey tape if you're so-inclined)
Bonus marks for colour-coordinating with your bike and car. Do the whole length of the rack upstand, not just the contact point.
Like this but on the upstand too, not just the tines.
You could put the protection on the bike, like this, but its more likely to fall off. Velcro cable ties can help here.
This isn't exactly what your are looking for but it is simple solution. I use cheap foam self seal pipe insulation of various diameters and put them on parts of bike that can be damaged during transport (fork, top tube, chain stay, etc) or you can fix it to your bike rack.
It is easy to put on/take off, can be used many times and it is really good to prevent collisions of parts if you transport more than one bike on the rack. Those pipe insulations come in lengths of usually 2 meters, with various wall thickness from 9 mm do 2 cm so you can choose ones which will fit your bike frame or rack.
With some racks, especially racks that hang the bike from its frame, Rack-Rash is a thing you learn to live with as its practically impossible to prevent. The price of cheaper racks is often (but not always) cosmetic damage to bikes.
In my experience, to prevent bikes getting trashed in transit, they need to be supported by the wheels using a quality rack design. Google "Wheel Support bike rack" for some good examples. I like ones such as the Yakima FrontLoader or Thule 594XT Sidearm that hold the wheel, not the frame - similar setups are available for rear racks.
I used to have a Saris Bones rack and ended up wearing right through the paint in several spots. I learned that simply wrapping a sock (or other cloth) around the tube/spot in question and tightening it in with the strap eliminated almost all the rubbing. For longer trips I would secure the padding with a zip tie or tape.
Pool noodles and pipe insulation are great, but be careful when the foam degrades or is in high heat (think black foam on a sunny day) as the foam can melt and stick to the bike (had this happen once)!