2002 corolla transmission noise

[elementofice]

hi i have a 2002 toyota corolla that drives pretty smooth but recently i found out that when i start the car after the car being parked for a few hrs or overnight, and i shift from park to reverse or drive, doesnt matter which, there seems to be a loud gear sound that wasnt there before. i have to put more strength into it to shift it from park. this only happens the first time after starting the car in the morning or something, after i shift a few times and after i start driving, the transmission shifting becomes smoother. is this because the transmission fluid is low and needs to be drained/refilled? because i recently drove from la to north california which is like a 6 hr drive, and i noticed after driving halfway when i stopped to take a break that there was fluid dripping from under the car. i thought it was the coolant fluid, but i checked that and the water was still full, so it most likely is transmission fluid leaking perhaps? does anyone have any opinions on this?

also another problem my cars been having for awhile now, the car vibrates when i drive around 65-70mph only, any lower or higher speed there is no vibration, i will drive up to 65-70 and it will vibrate, then accelerate to 80ish and the vibration mostly ceases. i went to a auto repair shop they said my front two tires were bad and that i needed an alignment, so i replaced those two tires and got an alignment, but it still vibrates. what do you think the problem can be?

thanx!