Yes,
No, you are free to define positive separately for each force, each displacement, each acceleration. Just be clear about it and do it consistently through the equations.
If all such variables are along the perpendicular axes, it is a good idea to pick one convention for them all. If not, you could decompose each oblique variable into such components or define the conventions individually.
Many prefer to guess which way each will act and define positive accordingly. That's ok as long as you handle each consistently and accept that some may turn out to have negative values.
That said, there may be cases where the equation does change if you guessed wrongly, but I can only think of quite contrived ones.