You can use 'runs test', Ljung–Box test or some other tests for serial correlation you find in SPSS.

The DW test will not detect serial correlation of orders higher than 1.

Yes, you can build the ARIMA model for that data then conduct diagnostic tests for the residuals.

Can i transform,  the data using Log and then run liner regression model again, knowing that on the same model i face heterosditicty and i use WLS 

Yes, you can. You need to provide more details about you model, then your question will be more clear.

i examine the relation between the operation cost and Fuel price data collect over years from 2001 to 2015 try to test relation between fuel and airline operation cost, i use OLS,  i first test linearity, then Homoscedasticity and then auto correlation.

Model give result show non Homoscedasticity so i used WLS, and run the model again but Durbin-Watson  show in one airline 0.870 when i check DW table it show  its autcorrelated what i want to know, i can use Log for the Y then i run WLS that would be acceptable on statistic point of view or not ( i am not have static back ground )

Yes, you can apply the log transformation if it helps you achieve constant variance for the residuals or a linear relationship between to two variables.

So in such case no need for the very complicated ARIMA model to run OSL

If you do not have autocorrelation in OLS residuals, it seems you do not need ARIMA.