To avoid voltage oscillations at the gate, do I need to include
resistors in between MOSFET and gate-driver?
The purpose of the resistor is to share power and to reduce overshoot (A side effect of ringing). This resistor value may not be necessary or it might be crucial. Your best bet is to just try different resistor values and see what works best. Often times a 0 Ohm resistor works just fine.
According to the datasheet, the gate driver can source up to 2.5A and
sink 5A, so is it the current when no resistor is connected between
the MOSFET and the gate-driver or we have to limit it to the given
current?
The gate driver is essentially a current source. It will provide that much current at whatever voltage it can.
The actual current at any time is found through analysis of the circuit. The circuit shown here is a simplified version of what is happening. It will give you a good idea of what the current is. In this example the instant the gate driver voltage goes high the current in the circuit will be 1.5A. Then the current will decay as the capacitor charges up.

simulate this circuit – Schematic created using CircuitLab
in the datasheet of MOSFET, it is given that the MOSFET gate
resistance is around 8 ohms, so should I connect external resistors?
Test the circuit. This largely depends on the physical layout of the circuit. Long traces add inductance and can lead to overshoot. So, if you see overshoot or ringing add a resistor.
If the resistor is required then a lot of power will be lost through
this resistor, is there any special resistor for this? or recommend me
any if you have any idea...
A resistor is a resistor it dissipates power. (P = I^2R) Reducing resistance without increasing current will result in less power dissipated.