4

There are a number of numbering questions asked, but I haven't found one that fits this particular need:

1. First section

1.1 Second level

A. Third Level (italic)
B. Third Level (italic)

2. Another 1st-level section 

2.1 Another 2nd-level section

A. Third level    
B. Third Level

In short, \subsubsection{} and \subsubsection*{} are numbered as letters A, B, C, Both the label and the title itself should be italicized.

4

I wouldn't do things this way. Since your \subsection* levels are enumerated with letters, they are regular numbered sections, so you should use \subsubsection. (If you don't like typing \subsubsection you can change it to something else (e.g. \let\lsection\subsubsection)). Then you can format everything simply with titlesec:

\documentclass{article}
\usepackage{titlesec}
\titleformat*{\subsubsection}{\itshape}
\renewcommand{\thesubsubsection}{\Alph{subsubsection}.}
\begin{document}
\section{A section}
\subsection{A subsection}
\subsubsection{A subsubsection}
\subsubsection{A subsubsection}

\end{document}

output of code

5

Changing of the sectional fonts: Change size of section, subsection, subsubsection, paragraph and subparagraph title

Adjusting the counter representation (somewhat relevant): Continuous v. per-chapter/section numbering of figures, tables, and other document elements

enter image description here

\documentclass{article}
\usepackage{sectsty}
\subsubsectionfont{\normalfont\itshape}
\renewcommand{\thesubsubsection}{\Alph{subsubsection}}
\begin{document}
\section{A section}
\subsection{A subsection}
\subsubsection{A subsubsection}
\subsubsection{A subsubsection}
\section{A section}
\subsection{A subsection}
\subsubsection{A subsubsection}
\subsubsection{A subsubsection}
\end{document}

Note that you may have problems using hyperref with non-unique counter representations.

For consistency, I've kept the sectional numbering without an ending period, since your \subsections seem to be void of them. If needed, one can add a period. Either way, either add it to all, or remove it from all.

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