I saw that my SD card is FAT16 formatted. In order to improve performance, can I reformat it as FAT32? What filesystems does Android support for external storage?
Yes, you should be able to use FAT32 with no problems. Android supports FAT/FAT16 and FAT32, and I believe raw / unformatted cards may work with some phones. You can also use EXT partitions but this requires some extra work, see for example how to use ext partition in my android?