"A movement along the Aggreggate supply curve indicates an increase in output therefore a probability to increase labour force, correct?"
no, a shift along the AS curve does not mean an increase in the labour force. It means that more of the existing factors of production are used, for example, a fall in unemployment.
"A shift in the AS curve indicates a shift in the PPF therefore meaning an increase in total output and therefore also increase in labour force?"
not necessarily the labour force. It could mean any of the four factors of production. And it doesn't just mean an increase in the quantity of factors of production, it could also mean an increase in the quality of factors of production e.g. increase in education and training leading to increased productivity leading to a rise in production and so the PPC shifts out.
"Also, with the question how would an increase in government spending affect economic growth, how can I apply it to boom/recession scenarios?"
not quite sure what you're meaning here. try to stick to the question because I don't see how the economic cycle comes into things. but everything the guy above said is logical and makes sense. However, his first two points are incorrect.