The air intake may give you like 2hp. Now if you did some other upgrades like a cat back exhaust etc.... you would get a little closer to 18hp gain. You will get a bit more gas mileage out of it.
Usually the front crankshaft oil seal wears out and wears a groove into the crank so either positions a thin new oil seal in another place on the crank or use a repair sleeve.
Merely changing a tire or a battery cannot cause the speedometer to stop working. There will be a cable that runs down from the speedometer that controls these functions.
Timing belt is a part of an internal combustion engine. It connects the crankshaft to the camshaft(s), which control the opening and closing of the engine's valves. In interference engines, a timing belt break could cause severe valve damage and damage to other engine parts.
If there is air trapped in the clutch system, it will prevent adequate pressure transfer to the slave cylinder/throughout bearing, which could cause the problem you describe.