What you are hearing is the hydraulic lifters before they come up in pressure and is normal for pretty much all Miatas.
This page has good information on hydraulic lifters and how they work.
http://www.miata.net/garage/hla/index.html
As for hearing them during running it could be that you are low on oil. I have noticed this a few times at AutoX events after the car has burned off some oil. Check the oil level and make sure it is full.
Teeth Chattering
battery is in the trunk, put the red to red and black to black and have the other car running to charge your battery and give it a couple mins then start your miata
Miata's tend to tick a little.You can try 5-30 oil at your next oil change but it's unusual for a Miata not to tick a little at start up.
Cracks in the clutch disk will cause the noise and a wore syncronizer in will not allow gear to mesh, more so in cold weather.
The places to purchase Mazda Miata parts are many and varied. The best place to start would be Go Miata. Failing that a good option would be Auto Trader or the auto section of eBay.
I do not believe there are any beginning with m. Lots of other words such as rowdy,chattering,boisterous, strident,clamourous
You likely need a new ignition coilpack. I had this happen with mine also.
Check engine light, low power, no start, runs rough, bent valves,Check engine light, low power, no start, runs rough, bent valves,
Valves
fuel pump could have gone bad , does it have fuel in the tank ?
The oil sits at the bottom of your engine in your oil pan. The oil takes a minute to build that pressure up and get the oil all through out the valves.
Why is Infinity G20 1995 occasionally not starting. I have to put it in neutural to start.