When parking and steering fully to the right, i get a conking/hooking sensation in the right front suspension. Furthermore the car is not stable in a straight line at high speeds and sways to one side when taking my foot of the accelerator at high speeds.

Where to start...? Mechanical and technical skills are good. Workshop available. Full knowledge of Alfa Romeo's, but novice on the Miata. :-)

 

Take it to an alignment shop and tell them to inspect it, unless you have your own alignment machine.

 

Get it aligned.

Also check the tyre pressures.
Uneven pressures at the rear can make it pull slightly under accel/decel

 

Get wheel bearings/brakes checked as well. Bad wheel bearings can make a knocking noise, and also cause the brakes to drag on a corner which leads to pulling. Broken sway bar end links also make for interesting handling characteristics.

 

Loose alignment bolt, worn bushings, bad alignment, or a list of other things

 

To add further detail to the "alignment" answer, for the sake of understanding, caster causes a sense of self centering to cars. Pretty much all cars use it, but when you don't have it other kinematics of the susp. geometry can cause the wheel to "catch." I'm certainly no expert but I'd assume scrub radius. A decent amount of caster covers this up. Also caster is good for camber, adds it when turning, meaning you can run less static. I'm surprised coming from mustangs how little caster y'all run.