Should we use use the present continuous form "would you mind if" to ask a polite question?
No, you should not. It is ungrammatical to say:
*Would you mind if I am sleeping here?
The sequence of tenses needs to be more like either this:
Would you mind if I slept here?
Would you mind if I sleep here?
Although some might take exception with one or the other of that pair, both are heard in the wild.