Are there any inventions/applications in our world based on QFT? Are there nowadays any actual devices or experimental applications which are based on the quantum field theory and if so, how are they related to QFT?
I could not find any similar question besides this one.
 A: QFT techniques are routinely used in the condensed matter physics for studying electronic transport, phase transitions, etc. Given the importance of the semiconductor technology and magnetism today, this is probably by far the most extensive application of the QFT to real life.
A: Experimental Applications
Take the LHC. We need to calculate what the various probabilities are regarding which particles are going to emerge from the collisions, for how long will they exist and in what way will some  decay into stable particles such as electrons and the lowest mass quarks.
Without QFT we could not calculate the probabilites of these events and processes occuring and compare them to experimental results.  
The actual calculations involved are far beyond my understanding, so I will recommend this post LHC data and mathematics of QFT and this link Scattering amplitude, link between quantum mechanics and QFT.
Slightly off topic, I might say that a practical application of LHC using QFT was to confirm the existence of the Higgs boson, and it did so. So the LHC might be viewed in practical application terms, sort of, as a gigantic microscope:)
A: US patent 7411772: Casimir effect conversion
Abstract:
Techniques in which a 1.sup.st force, field, or effect caused by a Casimir effect is converted into a 2.sup.nd force, field, or effect. The 1.sup.st force, field, or effect might be distinct from the 2.sup.nd force, field, or effect only in the net vector or might be distinct in other ways. For example, the distinction might involve substituting a torque for a linear force vector or converting a force, field, or effect associated with the Casimir effect into movement or into an electric, magnetic, or electromagnetic force, field, or effect. These changes preferably are caused by an independent element placed proximate or between to the Casimir effect surfaces. Preferably, the torque causes rotation (i.e., spinning) of an element. This rotation is significantly different from prior-art embodiment because energy does not have to be put back into the system to "reset" the structures. 
I am not sure though how useful that would be:-) There are several other patents related to the Casimir effect: https://books.google.com/books?id=knyyfeKUTTUC&pg=PA20&lpg=PA20&dq=Casimir+effect+patent&source=bl&ots=YZN5PZg6_5&sig=TasvbvdJb6oHGSK6HurkWUEbiKQ&hl=en&sa=X&ved=0CEAQ6AEwBWoVChMIxevBxca9xwIVhViSCh1Ccg0m#v=onepage&q=Casimir%20effect%20patent&f=false
