The definition of runway incursion only refers to the surface of the runway, there is no altitude above the surface involved. The FAA defines four types, and note under Cat D the word "incorrect":
- Category A is a serious incident in which a collision was narrowly avoided.
- Category B is an incident in which separation decreases and there is a significant potential for collision, which may result in a time critical corrective/evasive response to avoid a collision.
- Category C is an incident characterised by ample time and/or distance to avoid a collision.
- Category D is an incident that meets the definition of runway incursion, such as incorrect presence of a single vehicle/person/aircraft on the protected area of a surface designated for the landing and take-off of aircraft but with no immediate safety consequences.
The examples you give are, however valid but, need to be examined individually as potential airborne separation problems.
You cite crossing runways, so the detail is important. An aircraft or vehicle crossing the runway you are using is not an incursion, provided you are not landing or taking off. (i.e. you might be lined up, taxiing, or crossing). It also helps if you are aware of the other operation, indeed in the case that you are lining up, it is essential.
The altitude of the crossing aircraft, if airborne, becomes a problem for you, as the other pilot, if that altitude or manoeuvre will affect your flight. Even an aircraft overlying at 1000 feet could be a problem for a high performance departure, or lander going around, if the over flyer is travelling in the same direction you want to go! You might climb up underneath the other aircraft or catch it up.
The permutations are probably endless, but I hope this helps.