To specify the height of a multiline text fielf, use the optional argument height, such as
\TextField[multiline=true,height=6\baselineskip,...]{Comments}\
For vertical alignment, you could use \height which gives he height of a box, together with \raisebox, such as
\renewcommand*{\LayoutTextField}[2]{\makebox[6em][l]{#1: }%
\raisebox{\baselineskip}{\raisebox{-\height}{#2}}}
You could even adjust the default height of a multiline text field, like
\renewcommand*{\DefaultHeightofTextMultiline}{6\baselineskip}
Here's a complete example for this, re-using the code of the linked question:
\documentclass{article}
\usepackage{hyperref}
\renewcommand*{\DefaultHeightofTextMultiline}{6\baselineskip}
\renewcommand*{\LayoutTextField}[2]{\makebox[6em][l]{#1: }%
\raisebox{\baselineskip}{\raisebox{-\height}{#2}}}
%\renewcommand*{\LayoutTextField}[2]{% or this or similar ...
%\raisebox{-\height}{\makebox[6em][l]{#1: }}\raisebox{-\height}{#2}}
\def\LayoutChoiceField#1#2{\makebox[6em][l]{#1: }#2}
\newdimen\longline
\longline=\textwidth\advance\longline-6em
\begin{document}
\begin{Form}
\TextField[name=Name,width=\longline,borderwidth=0,bordersep=4pt,
backgroundcolor={.85 .85 .85}]{Name}\vskip1ex
\TextField[name=Affiliation,width=\longline,borderwidth=0,
backgroundcolor={.85 .85 .85},]{Affiliation}\vskip1ex
\ChoiceMenu[borderwidth=0,radio=true,
backgroundcolor={.85 .85 .85}]{Are you a}{Student, Academic}\\
\TextField[name=Comment,multiline=true,height=6\baselineskip,
width=\longline,borderwidth=0,backgroundcolor={.85 .85 .85}]{Comments}\\
\end{Form}
\end{document}

backgroundcolor, it changes the background color when I click on the field, but as soon I filled the field and press enter, the default background color comes back. Any idea why ? – joseldsm Oct 30 '18 at 10:38