Can I increase the logo size?

You can use custom CSS to adjust that. Please try the following:

#logo {
    margin-right: 30px;
    width: 30%;
}
#tagline-search-group {
    text-align: left;
    width: 65%;
}
@media only screen and (max-width: 1024px) {
    #logo {
        width: 350px;
        margin: auto;
    }
}
@media only screen and (max-width: 480px) {
    #logo {
        width: 100%;
    }
}

You can go to "Appearance > Customizer > Others" to put the code there.

In case you would like to use custom CSS for other elements, I would recommend Developer Tools on Chrome or Firebug on Firefox to inspect the elements on the page. Then you can know which CSS selector to adjust.