is there an implication that heck has a meaning of to have slight sex with someone
Nope. Heck is a neutered version of hell (which isn't too vulgar these days, but still "adults only" for the most part) and has nothing to do with fuck (which is still considered very vulgar).
Why the hell is she here? (inappropriate for children to say)
Why the heck is she here? (you could say this in front of children)
Screw is a popular "censorship-friendly" substitution for fuck and can be used in many but not all the ways fuck can.
For instance - you can say the fuck in the same way as you would say the hell - and fuck is much stronger ...
Why the fuck is she here? (vulgar and expressing a lot of hostility, cover the children's ears ...)
In this case the fuck has no connection to sex but is just an adverbial intensifier. You cannot use screw here. However, as seen above, you can use the heck.