At the moment there is even overcapacity in regards to testing as the german health minister announced yesterday. We could do more, but less demand than supply actually, so extensive testing of Bundesliga players should be doable. I heard it costs 2.5mln Euro for Bundesliga, so no biggie too. I still think, it's good to give it a try with resuming Bundesliga, but if that experiment fails, there will be huge shitstorm of course. But I think everything will be fine health-wise and lots of people will be happy with some football going on again (including me).
Such testing cost is feasible for teams because the financial benefits they can get back when Bundesliga resumes and finishes will be bigger. Costs have to be spent first and benefits will be get back months later. Players are strong guys and most of them will be fine even they get infected with the virus. There will be some cases will have severe conditions but not too many. With whole population, the CFR (case fatality ratio) for the young guys fluctuates about 0.2%. I think if we ask players that they want to resume the league and play or not, they will say yes.
I didn't come across such statistics with the antibodies. Hospitals and blood donour facilities have started calling recovered people to check for antibodies, but the tests seem to give false-positives more often than not and are not yet reliable. So people might feel kind of safe, when actually they are not. And capacity-wise the system is not yet ready for some antibody-testing-tourism, to have bigger sample sizes and draw more viable conclusions.
Thanks. False positive with antibody test is always a problem. Even with Realtime PCR test, there are false positive results too because of there are some steps to prepare and treat samples before going to test them.