If I employ someone to destroy a building, what is the net GDP impact? Can this one-off cases be extended? For instance, if I employ someone to destroy 50 buildings and rebuild them, does that contribute an increase in GDP?
It certainly does affect DGP, because what you destroy is part of the capital base $K_t$, while the building activity is part of gross investment. The capital base is not part of the DGP, while investment $I_t$ is.

A related question is, what is the net effect on the capital base? That will depend on the current value of the buildings being destroyed, compared to the value of the new buildings.  

The more interesting question is : how are we to classify the value of demolishing services alone? Labor and capital will be expended to bring down the old structures, so certainly production factors will get rewarded.

From an accounting point of view, these constitutes also part of the cost of the new buildings, and this has a wise economic rationale: the returns from the commercial exploitation of the new buildings, must be evaluated against the total cost incurred so as to be able to exploit them, and this includes the cost of demolishing pre-existing structures.  

Do the economics discipline treats such demolishing services the same way? yes, they are also part of gross investment.  

Assume now that we are only demolishing an old building, without building a new one. It seems a little weird to count the cost of demolition as "gross investment" that will increase GDP and tend to positively offset the reduction of the capital base due to the elimination of the old buildings. Investment to what? - we have not erected new structures.  

Well, what increases here by the demolition is the value of the land. Why? Because prior to demolition, the land was committed to a specific building, and so the land's uses were restricted. Now that the land is land only, it can be used for many more purposes than before. This has economic value.

Usually, when a piece of land has buildings, we see it as a whole, and we don't make the above distinction. But the distinction is there and justifies treating the cost of the demolition alone as investment.