You can change the size of the tablefootnotes by using any font switch you find in introductory books. In the example below i used Large and made it red, just to emphasize what changes.
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\documentclass[11pt, a4paper, oneside, onecolumn, openany]{book}\usepackage{etoolbox}\usepackage{parskip}\usepackage{showframe}\usepackage{mwe}\usepackage{threeparttable}\AtBeginEnvironment{tablenotes}{\Large\color{red}}%Make the%tablenotes red and Large. Or \footnotesize ;-)\newcommand{\species}[1]{\textit{#1}}%Helper command, keep it%flexible\begin{document}\chapter{Test Chapter}\label{chap:testB}Computational models are mathematical models of systems such asare found in biology, physics, weather systems etc. Such modelscan be used to predict the behaviour of these systems in aneffort to develop interventions which help to control ourenvironment. By predicting weather systems we can safeguardourselves against extreme weather conditions or plan our crops toavoid failures. In physics, models serve the purpose ofdiscovering the origins of the universe and predicting what thefuture might hold for us. In biology, computational models serveto provide a better understanding of the way our bodies work aspart of our effort to fight disease and prolonglife\footnote{stuff}.\blindtext[2]\begin{figure}[t]\centering\begin{threeparttable}\begin{tabular}{c}\includegraphics[width=.9\linewidth]{example-image-b}\end{tabular}\caption{From left to right: \species{Caenorhabditiselegans}\tnote{a}, \species{Drosophila melanogaster}\tnote{b},\species{Saccharomyces cerevisiae}, \species{Danio rerio}.}\label{fig:model_organismsB}\begin{tablenotes}\item [a] A footnote\item [b] Another footnote
Concerning the other boxed stuff. Can you make a minimal working example, so i can see what is going on? The code defines new floating environments for programs and directory listings. Do you need this stuff, or is it rubbish from an old template?