Can regular JavaScript be mixed with jQuery?

Yes, they’re both JavaScript, you can use whichever functions are appropriate for the situation.

In this case you can just put the code in a document.ready handler, like this:

$(function() {
  var canvas = document.getElementById("canvas");
  if (canvas.getContext) {
    var ctx = canvas.getContext("2d");

    ctx.fillStyle = "rgb(200,0,0)";
    ctx.fillRect (10, 10, 55, 50);

    ctx.fillStyle = "rgba(0, 0, 200, 0.5)";
    ctx.fillRect (30, 30, 55, 50);
  }
});