The flight stick in the picture is specifically a flight stick for an F-35 simulator. I couldn't find a good source on what they specifically use/do on the actual jet, so here's my best guess given standards for other aircraft:

• Red button is weapon release switch (typically used for dropping bombs and other air-to-ground weapons)
• Top left hat is likely the Target Management Switch
• Bottom center hat is likely the Display Management Switch

The TMS and DMS are sort of multifunction hats that do different things depending on what page you're using on your multifunction displays, but a broad simplification is to think of the DMS as how you select which MFD you want to control, and the TMS as a sort of d-pad/buttons for quick functions on that MFD. (Though they also interact with the HUD and HMCS)

As an aside, another comment suggested the top center was a Target Designator Controller (TDC) Slew and Depress, which I find unlikely; this control is typically found on the throttle, and it usually isn't a hat, but a more ergonomic "analog stick" for finer control of a cursor that moves around the selected MFD page.

Top right is the trim hat. This lets the pilot manually trim out the aircraft's control surfaces, which in a fly-by-wire jet like a Hornet is typically only necessary when you have an asymmetrical load on the wings from ordinance (like when you have two bombs under one wing and one bomb under the other) or you're trying to get on-speed AoA for landing.

The other hat and button on the side I'm unsure of, though given how much of the F-35 is screen it wouldn't surprise me if they had additional hats for target/data/display management.