RCM on employee travelling

RCM required only if you have made expense excess to Rs 5000 per day from an unregistered vendor. In your case no RCM required.

if there are 50 to 60 employees

then this condition is not applicable

if there are 60 employees, and all expenses are made from unregistered vendors, then you are required to deposit Tax on reverse charge. But for ease of the compliance, Authority allows you to raise a consolidated bill at the end of the month.

if we treated this fixed allowance as a part of salary then there is no gst liability.but that increases the income tax burden on the employee.is there any allowance which is exempt under income tax act and we give this fixed allowance under that head.
then our liability to pay gst will become nil and employee has no burden of extra income tax

first you must decide that expenses is part of salary or staff welfare.