1. Download WOWSlider wizard program for Win or Mac from
http://wowslider.com/wowslider-free-setup.zip

2. Create a slideshow in WOW Slider program and click "Publish" button, select "Wordpress Slider" as a publishing method:

3. Install and activate the created module – wowslider.zip as WordPress plugin:

4. WOWSlider menu will appear. Go to WOW Slider -> All Sliders and copy the shortcode of your slider:

5. Add the shortcode inside the page where you want your slider to appear:

6. Preview changes:

7. Use WOW Slider menu WOW Slider -> Add New to add each next slider.

See also WOW Wordpress Slider Plugin at WordPress.org

  I've recently ordered WOWSlider. Now I want to add it in Wordpress header. How i can do this?

To insert WOWSlider into header you should use WOWSlider PHP code.

Go to
WOW Slider -> All Sliders

and click on "Excerpt view" button at the top right corner. Additional line "for templates" with php code will appear under line with shortcode. You should add this php code into your header (Appearance->Editor->Header) into the place where you want your slider to appear, for example:

<?php wowslider(1); ?>

 How to add WOWSlider in Wordpress widget?

You should install a special plugin that allows to add php code into text widget firstly. For example, "daikos-text-widget":
http://wordpress.org/extend/plugins/daikos-text-widget/

After that go to
WOW Slider -> All Sliders

and click on "Excerpt view" button at the top right corner. Additional line "for templates" with php code will appear under line with shortcode. You should add this php code into "daikos-text-widget", for example:

<?php wowslider(1); ?>

  How can I change the DOCTYPE declaration for universal compatibility in Wordpres?

You should select
Appearance -> Editor
and change "header.php" from templates in the right column.

  Is it possible to make changes (add/delete images, change template or effect) directly in Wordpress?

No, it's impossible. You should make all changes in WOWSlider application and generate a new module.