Normally splines rather than screw on, though there will be screw under a cover to hold the handle on.
Splines look a bit knackered but a new handle ought to fit and the possibly bad assumption that they haven't changed the number of "standard" splines theer are over the years...
That's a composite kit with various collars and washers to enable the valve body fit 1/2" of 3/4" taps. At aguess you'll need the right hand collar and the smaller conical washer. You may need to remove the flat washer to fit the conical one. Not sure what open top hat things are for. Fiddle about and see where they fit?