$$
A=n_p+n_n
$$

$$
Z=n_p=n_e
$$

we conclude that the correct answer is A.

$$
n_p=28;, n_n=32;, n_e=28
$$

$$
^{A}_{Z}Xrightarrow ^{A}_{Z-1}Y+e^-barnu
$$

is called $beta$-decay so here the correct answer is B.

$$
^{A}_ZXrightarrow^{A-4}_{Z-2}Y+^4_2alpha
$$

$$
A=A_0cdot 2^{-frac{T}{T_{1/2}}}
$$

Now, we can substitute the given values to have that after 16 days

$$
^1_0textrm{n}+{^{14}_{7}textrm{N}}rightarrow{^{14}_{6}textrm{C}}+^{textrm{A}}_{textrm{Z}}textrm{X}
$$

for which we should find the unknown isotpe.

$$
A=1+14-14=1
$$

$$
Z=7-6=1
$$

so our mysterious element is $^1_1$H, i.e. the choice A.

$$
m=m_0cdot2^{-frac{T}{T_{1/2}}}=2.34times 2^{-frac{4times 365}{138}}=1.51times 10^{-3}textrm{ kg}
$$

so the answer is C.

$$
N_U=frac{Ntimes E_{TNT}}{E_{U}}=frac{20times 10^3times 4times 10^9}{3.2times 10^{-11}}=boxed{25times 10^{23}}
$$