Understanding mosfet drive voltage
Indeed \$V_{GS}\$ should not exceed the maximum rating of 20 V.

That 2.4 V is the maximum threshold voltage, so some devices may have a threshold voltage of 2.4 V. If you'd then apply a \$V_{GS}\$ = 2.5 V the "overdrive" would be only 2.5 V - 2.4 V = 0.1 V which isn't a lot. The MOSFET will probably not turn on fully.

What I usually do is apply a \$V_{GS}\$ that is the same or higher than the \$V_{GS}\$ that the manufacturer uses to specify \$R_{DS,on}\$. Here \$R_{DS,on}\$ is specified at \$V_{GS}\$ = 4.5 V and 10 V. Unless you really need the extra low \$R_{DS,on}\$ I would use at a \$V_{GS}\$ of at least 4.5 V.

Regarding the freewheel (or flyback) diode: you only need it for an inductive load, so relay coils, motors etc. For a lightbulb or LED strip the diode is not needed.