Conceptual question regarding the Laplace transformation
Both 1 and 3 are correct.  Both 2 and 4 are wrong.
1 is correct. By duality principle, multiplication in time domain corresponds to convolution in the frequency domain and vice versa.
3 is correct as LT provides us the complete response zero input (transient) and zero state
response (Steady State). By contrast, FT gives us only the steady state response.