Answer
See the detailed answer below.
Work Step by Step
$$\color{blue}{\bf [a]}$$
We know that the circular aperture causes diffraction, so the laser beam must spread out. In other words, $\bf No$, the laser beam can't be perfectly parallel.
You can test that by watching the point of the laser pointing pen in a wall that is 50 m away, you can say that the red circle on the wall is more than 10 cm in diameter while the pen is only 1 or 2 mm in diameter.
$$\color{blue}{\bf [b]}$$
We know, in a circular aperture, that the first dark fringe's angle is given by
$$\theta_1=\dfrac{1.22\lambda }{D}$$
Plugging the known;
$$\theta_1=\dfrac{1.22(633\times 10^{-9})}{1\times 10^{-3}}=\bf 7.7226\times 10^{-4}\;\rm rad$$
$$\theta_1=\color{red}{\bf 0.442}^\circ$$
$$\color{blue}{\bf [c]}$$
The width of the laser beam at some distance is given by the bright central maximum in a circular aperture.
$$w=\dfrac{2.44\lambda L}{D}$$
Plugging the known;
$$w=\dfrac{2.44(633\times 10^{-9})(3)}{1\times 10^{-3}}=\bf 0.00463\;\rm m$$
$$w=\color{red}{\bf 4.63}\;\rm mm$$
$$\color{blue}{\bf [d]}$$
And at 1 km,
$$w=\dfrac{2.44(633\times 10^{-9})(1000)}{1\times 10^{-3}} $$
$$w=\color{red}{\bf 1.54}\;\rm m$$
