The TAP II Controller has integrated WiFi and does not require a dongle.
No, TAP II, TAP Monitor, and TAP&Go all have integrated WiFi and do not require a WiFi dongle.
Unsure what type of controller you have? The original TAP Controller has the Start button and Menu button on the left side of the touchscreen. The TAP II Controller has the Start button and Menu button on the right side of the touchscreen.