You can reduce the font size to 10 or 11 points if the affiliation is long. If it is still too long, it will have to wrap to the next line.
The second alignment issue is due to centering. The affiliations will not left align because they are different lengths and centred. It looks better centred on the title page. Do you have a specific reason not to leave it centred?
If you must left align the affiliations, it's possible to pad the shorter line by adding tildes. Perhaos thee is a more elegant solution, but this will work. I couldn't find anything else it the package documentation that will allow left aligning instead of centring.
Code: Select all
\documentclass[11pt]{article}
\usepackage{authblk}
%\date{}
\title{PAPER TITLE}
\author[1]{FIRST AUTHOR}
\author[2]{SECOND AUTHOR}
\affil[1]{address university laboratory address xxxxxxxxxxxxxxxxxxxx.}
\affil[2]{second shorter address~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~}
%\renewcommand\Authands{ and }
\begin{document}
\maketitle
abstract
\end{document}