The given statements pertain to aniline, a primary amine where the amino group ($\mathrm{NH}_2$) is directly attached to a benzene ring. Let's analyze the statements:

Statement (I): The $\mathrm{NH}_2$ group in Aniline is ortho and para directing and a powerful activating group.

This statement is correct. The amino group ($\mathrm{NH}_2$) in aniline is an electron-donating group due to the lone pair of electrons on the nitrogen atom. It increases the electron density on the benzene ring, particularly at the ortho and para positions. This in turn makes the ortho and para positions more reactive toward electrophilic aromatic substitution reactions. Therefore, the amino group is considered to be an ortho and para director and is one of the most powerful activating groups in the context of electrophilic aromatic substitution reactions.

Statement (II): Aniline does not undergo Friedel-Craft's reaction (alkylation and acylation).

This statement is also correct. Aniline does not undergo Friedel-Crafts alkylation or acylation reactions. The reason for this is twofold: Firstly, the Lewis acid catalysts used in Friedel-Crafts reactions (such as AlCl$_3$) react with the amino group to form a complex that deactivates the benzene ring toward further reaction. Secondly, the strong interaction between the Lewis acid and the lone pair on the nitrogen can lead to a salt formation rather than the desired alkylation or acylation of the benzene ring. Moreover, the acidic conditions can lead to protonation of the amino group, converting it into an $\mathrm{NH}_3^+$ group, which is meta-directing and deactivating, further inhibiting the reaction.

Given this analysis, the correct option is:

Option A: Both Statement I and Statement II are correct.