HTML/Javascript Currency converter

Question 1

You need to remove var statements from initialize function and add them above this function:

var gbp, usd, eur, cad, aud;
function init()
{

    gbp = document.getElementById("GBP");
    usd = document.getElementById("USD");
    eur = document.getElementById("EUR");
    cad = document.getElementById("CAD");
    aud = document.getElementById("AUD");
    //...

In this case variables gbp, usd, eur, cad, aud will be visible in other functions scopes.

Probably you need to read more about variables and scopes. For example at MDN. Scopes and closures are very important in JS.

Question 2

I know this is old but I just happend upon it and thought you might like to know why your code still doesn't work even after antyrat's (correct) suggestion.

The issue lies with the clash between your variables and functions names.

There are some good articles explaining what actually happens when you do this offsite, such as here

Simple fix: change your function names...

var gbp, usd, eur, cad, aud;
function init()
{
    gbp = document.getElementById("GBP");
    usd = document.getElementById("USD");
    eur = document.getElementById("EUR");
    cad = document.getElementById("CAD");
    aud = document.getElementById("AUD");
}

function gbpfunc()
{
    usd.value = parseFloat(gbp.value) * 0.49246;
    eur.value = parseFloat(gbp.value) * 0.69714;
    cad.value = parseFloat(gbp.value) * 0.50221;
    aud.value = parseFloat(gbp.value) * 0.43497;
}

function eurfunc()
{
    gbp.value = parseFloat(eur.value) * 1.43448;
    usd.value = parseFloat(eur.value) * 0.70641;
    cad.value = parseFloat(eur.value) * 0.72037;
    aud.value = parseFloat(eur.value) * 0.62382;
}

function cadfunc()
{
    gbp.value = parseFloat(cad.value) * 1.99169;
    usd.value = parseFloat(cad.value) * 0.98054;
    eur.value = parseFloat(cad.value) * 1.38814;
    aud.value = parseFloat(cad.value) * 0.86613;
}

function audfunc()
{
    gbp.value = parseFloat(aud.value) * 2.29964;
    usd.value = parseFloat(aud.value) * 1.13262;
    eur.value = parseFloat(aud.value) * 1.60329;
    cad.value = parseFloat(aud.value) * 0.88297;    
}

function usdfunc()
{
    gbp.value = parseFloat(usd.value) * 2.03032;
    eur.value = parseFloat(usd.value) * 1.41544;
    cad.value = parseFloat(usd.value) * 1.01941;
    aud.value = parseFloat(usd.value) * 0.88297;
}

init();

<input type="text" id="GBP" size="10" value="0" onchange="gbpfunc()"/>
    <label for="GBP"> GBP </label>

    </br>

    <input type="text" id="USD" size="10" value="0" onchange="usdfunc()" />
    <label for="USD"> USD </label>

    </br>

    <input type="text" id="EUR" size="10" value="0" onchange="eurfunc()" />
    <label for="EUR"> EUR </label>

    </br>

    <input type="text" id="CAD" size="10" value="0" onchange="cadfunc()" />
    <label for="CAD"> CAD </label>

    </br>

    <input type="text" id="AUD" size="10" value="0" onchange="audfunc()" />
    <label for="AUD"> AUD </label>

Question 3

We can delegate and try to keep the DRY principle

const conv = { "gbp": { usd: 1.39, eur: 1.17, cad: 1.75, aud: 1.80 }, "eur": { gbp: 0.86, usd: 1.19, cad: 1.50, aud: 1.54 }, "cad": { gbp: 0.57, usd: 0.79, eur: 0.67, aud: 1.03 }, "aud": { gbp: 0.55, usd: 0.97, eur: 0.65, cad: 0.97 }, "usd": { gbp: 0.72, eur: 0.84, cad: 1.26, aud: 1.30 } };

const formatVal = num =>  {
  const dec = num % 1 ? 2 : 0; // https://twitter.com/wesbos/status/1369713969007575043
  return (num).toFixed(dec);
};
window.addEventListener("load", function() {
  const fs = document.getElementById("fs");
  const fields = [...fs.querySelectorAll("input")].reduce((acc, fld) => (acc[fld.id.toLowerCase()] = fld, acc), {})
  fs.addEventListener("input", function(e) {
    const tgt = e.target;
    const from = tgt.id.toLowerCase();
    let fromVal = +tgt.value;
    Object.entries(conv[from]).forEach(([key, val]) => fields[key].value = formatVal(val * fromVal));
  });
});

fieldset {
  width: 150px;
}

input[type=number] {
  text-align: right;
  width:80px;
}

<fieldset id="fs">
  <label><input type="number" id="GBP" value="0" autocomplete="off" /> GBP</label></br>
  <label><input type="number" id="USD" value="0" autocomplete="off" /> USD</label></br>
  <label><input type="number" id="EUR" value="0" autocomplete="off" /> EUR</label></br>
  <label><input type="number" id="CAD" value="0" autocomplete="off" /> CAD</label></br>
  <label><input type="number" id="AUD" value="0" autocomplete="off" /> AUD</label>
</fieldset>