So... how is there no gravity at the center if gravity is decelerating the object? See my previous post.
Once past the centre your velocity would decrease as gravity started to decelerate you. Eventually the gravity would reduce your velocity to zero and then would start accelerating you back towards the centre. Hence your velocity would still be at it's maximum when you go through the centre.
Because at the instant you were at the centre (bearing in mind it's an instant due to your velocity) the gravity would be acting equally on each point of your body pulling towards a point you already occupy. The net effect would be that your acceleration due to gravity would be zero, not that there would be no gravity. Once your velocity is taking you away from the centre the acceleration due to gravity would be acting in the opposite direction (decelerating you) and reducing your velocity. Eventually that deceleration would reduce your velocity to zero and then start pulling you back towards the centre.
Obviously this is all assuming you can engineer a tube that could be run all the way through the earth of course! Which is quite impossible with any technology we currently possess.