When you break apart a clock, you see all of the pieces that come out and conclude that they were the parts of the clock. When you break apart a nucleus and see a bunch of quark-antiquark pairs, many people would conclude that a nucleus is made up of quarks. read more
In QFT, these particles don’t really exist as particles, but as bits of energy in fields. This also accounts for wave-particle duality as you describe, as the ‘wave’ of a ‘particle’ is just an oscillation in the field. read more
Virtual particles are indeed real particles. Quantum theory predicts that every particle spends some time as a combination of other particles in all possible ways. These predictions are very well understood and tested. read more