Interesting that available bird seed stops blackbirds digging moss. I did not think they ate seed. I believe they eat fruit and invertebrates. I've never seen them at a feeder.
There used to be a theory that one should plant extra fruit trees so the birds could have some and you could have the rest. Seemed to work OK for a couple of years but inevitably the increased food meant increased survival and a build up in numbers until the birds were eating both theirs and mine again.
Blackbirds have increased in our garden from just a couple to over 20 now, despite regular open warfare. Inevitably the population pressure pushes one into my bonsai patch again.
When they are nesting the male will sing or call every evening within 10 metres of the nest . The nest will be in a bush . They are very territorial if the nest is disturbed they move on . Another will take its place in time .
I've found it quite difficult to locate nests despite thorough checks of all likely bushes. Then when the leaves drop there they are

Very well camouflaged.
Not all nests are in bushes. These are very opportunistic and will build in any suitable location. I've regularly found blackbird nests among the starter trident maples in pots on the nursery benches - usually after the chicks hatch. Maybe I'm just not observant enough but I can't work out how they manage to build a nest and incubate eggs while I'm there every day.
Removing eggs just means the pair will start again straight away somewhere nearby. Our local environment officer told me he borrowed the eggs, lightly boiled them and returned them to the nest so the birds wasted a few weeks trying to hatch dead eggs. That delays breeding for a while but if I locate an active nest I'm more likely to lay in wait and remove the adult(s) which delays breeding more permanently.