” Are antibody tests a reliable indicator of previous infection or not? Is the statement ‘other elements of the immune system which do not produce antibodies may fight off a virus’ correct or incorrect? etc etc?”
First. The antibodies: they can be reliable in some diseases such as for example HIV and others as an indicator of a past or ongoing infection but they have to be worked out for each infectious agent, In the case of SARS-cov2 this has not been worked out fully as far as I know and it is ongoing work. The other problem is that you can develop antibodies but they can also fade away with time, and the time interval can be variable. It is also true that for viruses there is another measure for immunity and these are called T cells. They are lymphocytes that are primed to kill cells infected with viruses, for example. You cam also look for these but this is not as easy as looking for antibodies. In addition there are also what is called ‘natural killer cells’ that do not need priming by previous exposure but act against antigens commonly found in some bacteria and viruses, or activated through non specific immune interactions.
What Yeadon also discusses is cross reacting antibodies (and also T cells). These are antibodies that are not found in those exposed to SARS cov2 but who has been exposed to other corona viruses. There are 4 known corona viruses that cause the common cold (amongst other viruses). Because they are related they may have some antigens in common, but quite often you can account for these by designing the tests to be more specific, which is one of the problems we started with.
Where Yeadon fails to convince, in my view, is that he claims that there is sufficient evidence that these antibodies and T cell responses are present in the population in sufficient numbers, he quotes a figure of around 30%, but really without evidence, It is as if he proposes a hypothesis, but without any evidence, then reaches a conclusion.
As to Ioannidis, he is a true scientist with many achievements. He has taken the view, with some evidence, that because the IFR is low (he says about 0.2%) and because in studies performed by him and others there is a high proportion of people already exposed, because antibody tests show they do, then about 30% are immune and that the next wave will not be very bad. The problem as discussed above is how much do we depend on the accuracy of the tests, and also we still don’t really know whether the presence of the antibodies translates to protection from infection, or how long they last, hence the doubts cast on his recent work. Also his study recruited through Facebook ads, which means that the subjects were self selected. Hope that answers some of your questions.