Just a sec Shibin, you seem a bit confused...
FBT is attracted if all the following conditions are satisfied as per Q. 1 of CBDT circular 8/2005:-
1. There is employer-employee relationship.
2. Employees based in India.
3. Is a person (as per Income Tax Act) not being individual or HUF.
4. Income is not exempt u/s 10(23C) of Income Tax Act or is a fund/ institution/ trust not registered u/s 12AA of the Act.
5. Contributes to approved superannuation fund on employee behalf or provides free/ concessional ticket for employees/ their family's private journeys.
6. Whether he carries out business or profession or even activity which is not for profit or gain, if he incurs expenses of the nature specified in S. 115WB(2)
So from the above you can see that a person who is not liable to tax may very well have to pay FBT if he satisfies conditions. But, a person exempt/ registered as in pt.4 would not be liable to FBT, so there is no question of any relation between liability to IT and payment of FBT.
For the second part of your first question, Q. 83 of the same CBDT circular clarifies that the rate FOR THE PURPOSES OF FBT shall be the Income Tax Act rate. So, there is no attempt to distinguish between the depreciation rates under the two Acts for FBT purposes based on liability to tax.
Finally, loss on sale of car as per books is disallowed as expense under Income Tax Act as it is considered under Capital Gains head instead of Profits/ gains of business/ profession. Also, there is no express provision that taxes it to FBT