Modern Vespa

Where can I get the water pump screws (M5x21mm/part #015856) in socket hex form (I am not sure of the threading type they use)?

The size of the hose used to bleed the air?

A thick grease to hold the O-Ring?

The screw to open the compartment where you put the coolant is totally loose in my scooter (no matter how much you screw it), it feels like the housing of the screw has detached from the body or something. What can be done?

if your thermostat housing is loose due to a screw and wont tighten im afraid you need to pay someone to rethread it

If the screw won't tighten, your dealer or most hardware stores or auto store can sell you a new flat spring steel nut. It simply pushes into place just under where the screw goes in. Your existing flat nut has either dropped off, it happens, or the thread has stripped. Either way it takes 20 second to replace it..

a thread where they discussed sourcing the bolt How I extracted a stripped waterpump cover bolt

I used a 1/8" ID flex plastic hose. It was a little tight, but could be bigger.

Use silicone grease I bought Danco Silicone Grease, 88693 https://www.amazon.com/gp/product/B000DZFUPC/ref=oh_aui_detailpage_o03_s00?ie=UTF8&psc=1

He didn't strip his thermistat screws he just want to replace them weith Hex head bolts.
Try Fastenel, you'll have to buy a whole bag ot box, they won't sell you only one.

The screw that just keeps turning it the engine access cover screw.
just needs a new flat nut.

I may be mistaken but I think they are available on scooterparts.com

Exactly.

However, one of the last times I replaced the cover, it wasn't tightening, and on inspection, the nut was still there, just out of place. So before you panic, just have a look to see if it's still there....realign and install. If there's nothing there, you'll definitely need a new one.