Answer
See the detailed answer below.
Work Step by Step
$$\color{blue}{\bf [a]}$$
To answer this question, we need to know the time the light would take to travel the 100 ly, where ly is the time light travels in one year.
So, the light from Alpha would take 100 years to reach Alpha.
And since the explosion of Beta occurred only after 10 ly, there is no relevant between the explosion of Beta and Alpha.
$$\color{blue}{\bf [b]}$$
Let's assume that $\rm S$ is the galaxy’s frame and $\rm S′$ is the alien's frame.
We know that the spacetime interval between the two events is invariant in all frames.
So
$$s^2=(c\Delta t)^2-( \Delta x)^2=(c\Delta t')^2-( \Delta x')^2$$
$$ c^2(\Delta t)^2-( \Delta x)^2=c^2(\Delta t')^2-( \Delta x')^2$$
Solving for $( \Delta t')$
$$ (\Delta t')^2= \dfrac{c^2(\Delta t)^2-( \Delta x)^2+( \Delta x')^2}{c^2} $$
$$ (\Delta t')=\sqrt{ \dfrac{c^2(\Delta t)^2-( \Delta x)^2+( \Delta x')^2}{c^2} }$$
Plug the known, where $c= \rm 1\;ly/y$
$$ (\Delta t')=\sqrt{ \rm \dfrac{\frac{(ly)^2}{y^2}(10\;y)^2-( 100\;ly)^2+( 120\;ly)^2}{\frac{(ly)^2}{y^2}} }$$
$$ (\Delta t')=\color{red}{\bf 67.1}\;\rm year$$
