For question 1, I think that investment has a demand-side effect on the economy. I think it isn't a supply-side effect because it isn't stated that the investors are responding to a supply-side shock. So I'm saying that AD shifts right. With shifts in the curves, there will be a change in equilibrium. For example, the process you described of both curves shifting right will lead to higher output (even though the price level might not change).
That being said, the "foreign" part of the question does make things a little less obvious. Why would the question want to emphasise the foreign part of this investment? An improvement in technology in one firm will eventually trickle to other firms (vertically or horizontally). Technological improvement shifts the supply curve rightwards, but because this is a long-term effect, I did not say in the first paragraph that there is a shift of the supply curve. Also, if a foreign country sends its profit to its home country, there is effectively a small decrease in the demand curve, but on the whole that would be small enough that it would not offset the increase in demand that the investment brings.
The second question is obviously trying to highlight a decrease in supply, as you have said. The quantity of labour decreases; production decreases.
But... to throw a spanner in the works... this does sort of imply that the workers are consumers. If consumers leave the country, consumption decreases, which decreases aggregate demand (as you have said). One needs to know why the people needed to leave. That being said, with the word "workers" I think the question wanted to highlight the supply side effect.