Yes they do, they don't have their own nests as they all live in clocks
Do Cuckoos Really Lay Their Eggs In Other Birds' Nests?
Yes, the entire cuckoo family of birds are notorious for their parasitic habit of laying their eggs in other species ' nests. The Eurasian cuckoo, which breeds throughout Eurasia and migrates to Africa and southern Asia in winter, lives as a parasite by relying on many different birds for its upbringing. It uses upwards of a hundred different species.
Some other cuckoo species are not parasitic, however, they build their own nests and both parents rear the young.
Cuckoos are also not the only birds to have this habit, although they do suffer the worst of the reputation for doing so. The black headed duck, the parasitic weaverbird, the brown headed cowbird and the honeyguides all also lay their eggs in foreign nests. In each case, they lay their eggs in the nests of species from their own classification grouping, not just any other nest. It is only cuckoos that have evolved to be able to choose any other nest for their offspring.
Some other cuckoo species are not parasitic, however, they build their own nests and both parents rear the young.
Cuckoos are also not the only birds to have this habit, although they do suffer the worst of the reputation for doing so. The black headed duck, the parasitic weaverbird, the brown headed cowbird and the honeyguides all also lay their eggs in foreign nests. In each case, they lay their eggs in the nests of species from their own classification grouping, not just any other nest. It is only cuckoos that have evolved to be able to choose any other nest for their offspring.
Yes do and they will also kill other birds eggs
Yes this is true .