As per I understand You have blog posts with category. The category structure will be 

#Category
- Child category
-- Child Child Category
--- Child Child child Category
----
-----
------
and so on.

Q1: Is this category is the default wordpress category?

#Now you want to create a form from the backend/ admin panel. Then you will select the category(ies) for each form. That means a form can be showed under multiple category. So when an admin select the category for a form then you the form will be displayed in all post under the category.

#each form has multilingual option( two languages ).

# A form can be accessed by three types of people

i) The general user  
ii) The registered user
iii) The admin ( who can create, edit, delete form )

# Foms fields

i) Text Box
ii) Radio
iii) Drop down menu ( select )
iv) File upload box ( browse button )
v) Check Box
vi) email field
vii) number type ( is this just take numerical input only ? )
viii) Google earth pointer

#Form Features - 
controlling tabs order which tab is up and which tab is down (need to be user friendly)

Q2: would you please just give me a detil idea about this section.

Choosing form for multiple categories

Form will effect the following page - 
1- index.php
2. Category page
3. search result Page
4. Printing page ( would you please give me some idea about this page? )
5. Data inserting page ( would you please give me some idea about this page? )
6. Details page - Singe page I thought