Try being explicit about all the border properties. For example:

border:1px solid black;

See Border shorthand property. Although the other bits are optional some browsers don't set the width or colour to a default you'd expect. In your case I'd bet that it's the width that's zero unless specified.

Two ways:

<img src="..." border="1" />

or

<img style='border:1px solid #000000' src="..." />

Yes, but it's not a div, it's a fieldset

fieldset {
    border: 1px solid #000;
}

<fieldset>
  <legend>AAA</legend>
</fieldset>

I cleaned up the HTML a bit, and the border is working fine jsFiddle:

<div class="ghassar">
    <div id="op">
        <label>Number of days</label>
        <select name="days">
            <option>1</option>
            <option>2</option>
            <option>3</option>
            <option>4</option>
            <option>5</option>
        </select>
    </div>
    <div id="add-to-basket">
        <input type="submit" value="Add to the basket" name="rent" id="buttom1" />
    </div>
</div>

and how can i make space between the content without using the tag <br>

You can use margins, like I did here:

#add-to-basket { margin: 50px auto; position: relative; }

and for the div tag shall i use class or id

It depends on what you're doing. Elements on the page can't share the same id, but multiple elements can have the same class.

Update: As mentioned in the other answers, you should also set the border color if you don't want the default. You can do that either with the shorthand way:

border:2px solid #f00; /* #f00 is the color red*/

or

border-color: #f00