For the URL Link box, you can do that one of two ways: CSS or standard HTML. If you are not familiar with CSS, I would suggest you use standard HTML. Simply modify your URL's input tag to include the "size=somenumber" where "somenumber" is the length of the text box, in characters. For the embedding code, which direction are you trying to change (vertical or horizontal). You can normally adjust those widths using the "rows=somenumber" and "cols=somenumber"

As for your second question, you can remove the recent tags from your main page by editing the "right.tpl" file in your templates directory.