Thayer, vol. 1, p. 53 notes that birth date is uncertain and that only the baptism record survives. The generally accepted date of the 16th is based on the fact that children in Bonn were usually baptized one day after birth.
Although high concentrations of lead were found in Beethoven's hair, it might have been only a contributor to Beethoven's demise. Other causes speculated on include: syphilis, typhus, and auto-immune disorders (such as systemic lupus erythematosus).
§ Remains
Beethoven was originally buried in the cemetery at Währing, but his remains were moved in 1888 to Zentralfriedhof