[Sofia]

For the quote problem, delete in your additionnal css:

.bbcode-start {
    border: solid 1px #BCBDC0;
    margin: 3px 20px 3px 20px;
}
.bbcode-header {
    background: #E0E0E0 url(images/ca_morpheus/misc/bg_bbcode.gif) top left repeat-x;
    border-bottom: solid 1px #BCBDC0;
    padding: 3px;
    color: #000000;
    font-size: 10px;
}
.bbcode-header .smallfont {
    font-size: 10px;
}
.bbcode-content {
    padding: 3px;
    background: #FFFFFF url(images/ca_morpheus/misc/bg_bbcode2.gif) top left repeat-x;
    color: #000000;
}
.bbcode-poster {
    color: #000000;
    padding-bottom: 4px;
    font-size: 12px;
}
.bbcode-poster strong {
    font-weight: normal;
    color: #000000;
}

Edit your template bbcode_quote and replace all your code by:

<div style="margin:20px; margin-top:5px; <if condition="$show['iewidthfix']">width: 100%;</if>">
    <div class="smallfont" style="margin-bottom:2px">$vbphrase[quote]:</div>
    <table cellpadding="$stylevar[cellpadding]" cellspacing="0" border="0" width="100%">
    <tr>
        <td class="alt2" style="border:1px inset">
            <if condition="$show['username']">
                <div>
                    <phrase 1="$username">$vbphrase[originally_posted_by_x]</phrase>
                    <if condition="$postid"><a href="showthread.php?$session[sessionurl]p=$postid#post$postid" rel="nofollow"><img class="inlineimg" src="$stylevar[imgdir_button]/viewpost.gif" border="0" alt="$vbphrase[view_post]" /></a></if>
                </div>
                <div style="font-style:italic">$message</div>
            <else />
                $message
            </if>
        </td>
    </tr>
    </table>
</div>

For your other problem (icons), it's because I don't use any post icons for this style. Post icons used are in the original folder. You must upload the original icons folder (vB) to "images/icons"