I will not fix it to you but i will try to put you in the right direction.
First thing i could notice is that you don't have a div(or any element) with the ID="divStyle".
The second thing is that you are probably receiving error messages because there are no one option active in the SELECT list
Third, you could use a single quote ' inside double-quoted "" strings.
Fourth, Here..
$("#divStyle").append("<div class="\"draggable\"" id="\""" imgid=""><p class="\"text\"">" + $("Textbox1").val() + "</p></div>");
you have forgoten to add the "#" to the selector
$("Textbox1").val()
$("#Textbox1").val()
Fifth, if you need a counter you could use a var instead of always be reading and parsing an element's text, and is a good practice to pass the radix to the parseInt function -> parseInt("10", 10)
http://www.w3schools.com/jsref/jsref_parseint.asp[
^]
Sixth, your button
<button class="styleButton" onclick="AddElement()">Přidat</button>
should have the type "Button"
<button type="button" class="styleButton" onclick="AddElement()">Přidat</button>
or, because it's inside a form, it will always cause a post-back.
And try to avoid writing inline javascript code. You are using jQuery there are some other ways to add click handling functions
hope it helps, and please let me know if don't.