Exam with 18pt main font

I'd simply add \usepackage[20pt]{extsizes}:

\documentclass{exam}
\usepackage[20pt]{extsizes}

\usepackage{showframe}% just for the example

\begin{document}

\begin{questions}
 \question First Question
 \question Second Question
\end{questions}

\end{document}

The same with extsizes commented out:

As for the title page, lack of an example makes it difficult to give advice.

With extarticle from extsizes you can increase the font size up to 20pt in the entire document. To load the font options from this class to the exam class you can create a customized document class, lets say, myexam.

You need to create a .cls document in your editor with the following code

\NeedsTeXFormat{LaTeX2e}
\ProvidesClass{myexam}[YYYY/MM/DD My exam class] %Current date

%%Preliminary definitions, needed by the options
\LoadClass[a4paper,18pt]{extarticle}

%%This parts handles the options passed to the class.
\DeclareOption*{\PassOptionsToClass{\CurrentOption}{article}}
\ProcessOptions\relax

%%Body of the class, most of the declarations appear here (if necessary).
%

Once you have created it, you can call as usual at the top of your preamble with

\documentclass{myexam}

P.S.: You can consult the following questions for further information

1. Difference between \LoadClass and \LoadClassWithOptions
2. How to set default font size in latex cls file?

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Also there is other package for exams named exam-n package, that has the option largefont for font size of 18pt. You can consider get familiar with this other package if useful for you.

The other answers here are cleaner, but for posterity I'm posting the hackier solution we implemented in the limited time we had.

We used the \fontsize command (see, e.g., https://tex.stackexchange.com/a/4140/60034) to change the font size to 18pt (with 22pt baselineskip) after the cover page content, using:

\fontsize{18pt}{22pt}\selectfont

It actually took a fair bit of work to tidy things up afterwards (oversize tables and paragraphs needing manual line breaks, adjusted page breaks, etc.) that required us to make a copy of the entire exam script source and edit it specially. So while the the source was rather neatly implemented as multiple files (one per question) \inputted from a top-level document this special version did not lend itself to a single-line solution.