I actually have three questions:

If any time remains or if time remains, which one is true?

For example:

If (any) time remains we will take a look at that

or "we take a look at that"? (In the latter part of the sentence, should we say we'll or we?)

And my last question is: can anyone suggest any other phrases to express this kind of situation? I mean if I have a number of certain things to do within a limited time, and I'm offered to do something else, how can I express my situation in terms of being able to spare time for things other than my main job? What are the ways of saying this?

With my time being limited, it depends if time permits to do other job requests