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.
$("#divStyle").append("<div class="\"draggable\"" id="\""" imgid=""><p class="\"text\"">" + $("Textbox1").val() + "</p></div>");
you have forgoten to add the "#" to the selector
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)
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.
hope it helps, and please let me know if don't.