1.
Antibodies are proteins that your immune system makes to help fight infection and protect you from getting sick in the future. When you are infected with a virus or bacteria, your immune system makes antibodies specifically to fight it. Your immune system can also safely learn to make antibodies through vaccination. Once you have antibodies to a particular disease, they provide some protection from that disease. Even if you do get sick, having antibodies can protect you from getting severely ill because your body has some experience in fighting that disease. How long this protection lasts can be different for each disease, each person, or influenced by other factors. Antibodies are just one part of your immune response.
2.
Three-dose VE is about 88% for Pfizer's mRNA vaccine against COVID-19 infection. (To tack onto the answer for #1: on the whole, antibodies are f--king
great.
3. You shouldn't be able to. But answering this in practical terms is difficult because a negative test tells you the result of the test
at the time of the test.
Let's say you come into contact with someone who is positive. You test afterward and test negative; how long after contact did you test? A few hours or even the next day in some instances might not be enough time for your viral load to build to the point of finding the virus through a PCR or rapid antigen test (and the FNR of rapid tests also has some impact here). You may also test too late; if you are positive for a very short period of time (thanks to antibodies making short work of the virus) you might actually test
after your immune system has cleared out the virus. You were positive, but you tested when you were already negative again.
You
should not be able to infect others if your viral load is so low that you test negative in the first place. Whether or not you're negative at the time of contact is a whole different thing and much harder to nail down.
If you think you have reason to be concerned, there is no harm in distancing or wearing a mask to mitigate that risk (or even just staying home for a couple days if you're really worried). But I think you'd be in a minority of people who wouldn't take their test at face value.