I'm new to Honda and have issues with a 1996 Honda accord with an Auto Transmission. When I drive my car the gears changes normally, however, If I floor the gas pedal on first gear it doesn't shift gear to 2nd and gets stuck at 5k rpm. Lastly, when my engine is on there is a leakage coming from the drive shaft that is connected to the front differential. Please help, thanks in advance.

 

Seems like your auto tranny is leaking fluids causing it to not go into different gear. Did you check to see how much fluid is in your tranny?

 

Do your CEL and D4 lamps work?
Are either of them blinking?
Have you checked for codes?
*Behind glove box door, remove two wire blue connector, jumper it with a wire, turn ignition to II(ON), watch for the CEL or D4 lamp to blink any codes*

Does the car have any other unusual driving issues?

Check your throttle cable adjustment, verify it is correctly adjusted and doe not have slack. This will limit the ability to fully open the the throttle.
Check the transmission throttle cable from the TB to the transmission, it should not have any slack, nor have any tension. Adjust it so that when the throttle body opens the lever begins to pull up.

If you have a leak coming from the differential where the axles are installed most likely the seals are leaking. Replace them.