Don't get confused between IFR separation (e.g. reduced separation in the vicinity of an aerodrome) and what might be called general aerodrome control, which is not quite so clearly defined.
As to the original question - local procedures may refine any rules of thumb, but the tower controller should not line up a departure unless there is sufficient time to get it away (and, technically, past the upwind end of the runway) before the inbound reaches the landing threshold. Amongst the other factors already mentioned that will affect the minimum range of the inbound I would include the location and distance from the runway of the holding point. And then add a bit for comfort incase the inbound goes around.
But as BigBoeing points out, it's largely what a controller gets paid for.
If the inbound goes around, technically it's essentially an Approach problem! Having said that, use of a reduced separation in the vicinity of the aerodrome may become very useful in such circumstances - which is why the decision whether or not there is room to get a departure away is affected by weather.
On the second question - just as you have to judge whether there is room to get the departure airborne before the inbound gets to the runway you can add a bit to let the departure get past the upwind end too. In practice though, certainly at busy airports, it seems common practice to be happy if the wheels of the departure are off the ground by the time the inbound crosses the threshold. But this means that there always has to be a plan for the go around!