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Answering specifically to your questions - chances of having infection with a single anal encounter (with a positive male ) is about 0.08 % per act. This is actually very low to result in a actual infection. With every subsequent act, you can just add them up, and the risk increases.
But the actual risk of infection, even with 3-4 encounters would be very less. For a infection to be passed it should be long term partnerships.
Acute HIV symptoms usually present after 4-6 weeks of exposure. They can last from 2-3 weeks or even more in some cases. Any person, who actually has symptoms due to HIV infection will definitely be positive for HIV antibodies. If you have symptoms and the test is negative, it does rule out HIV as a cause for the symptoms.
About 80-90% of individuals with positive infection show antibodies within the first 12 weeks of exposure. Hence any negative test done before 4 weeks should be confirmed with a repeat test after 12 weeks.