If it is a series motor it will/should have four connections to it. two of these will be to the field coils and two will be to the armature.
Normally you would connect one end of the field to the supply, the other end of the field to one end of the armature and then the other end of the armature to the supply.
The field and the armature are in series with each other, hence the name of the motor type.
To reverse the direction disconnect the field connections and swap them over with each other.
Coupling the motor to the diff instead of to the transmission will affect the performance of the car. This is because the gear ratios have changed and may not be suitable for the torque/power curve of the motor. It is one reason why most people keep the transmission intact even though only tow or three of the gears are used and infrequently at that.
The slow acceleration may be because the ratio is too high for the motor to be able to pull, it may not have the torque.
The lack of top speed may be because the ratio is too low, hence the need for a selection of speed.
Also it will depend on the voltage and controller set up too.
The loss of range may be because your motor is now pulling high amps at low rpm, where it is less efficient, when you are trying to move off. This is again down to not having gear ratios to allow the motor to spin faster when it is under load and to keep spinning at high speed as much as possible regardless of road speed.
Someone with more experience may come along and talk you through the rest.
