Lets address your questions one by one:
**1. Does the sentence start at the bottom right side of a page or paragraph? So if you are writing in a note book, how does this work?
**
It starts from right to left on same line. No ups and down like Chinese / Japanese. I remember anger of my teachers, as I used to write teRha meRha ( not in line) 
Here is example of Urdu sentence written from write to left. After a line ended, a new sentence (or incomplete sentence) starts in next line from right to left.
اردو اچّهی زبان ہے۔
2. What do you use for ending a sentence? Is there a period as in English or some mark as in Devnagari- like (|) ?
In Urdu, we use hyphen (-) for completing a sentence. Use of (,) ( ; ) (?) (!), etc is similar to English.
کراچی کس طرف ہے؟
3. When you are writing local languages like Sindhi in Arabic/Persian script, how do you compensate for pronunciation?
Its denoted by some signs know as Harkaat ( movements on letter- It includes Zer, Zabar, Pesh, etc)
example of Harkaat: **اُ ر دُ و
**There are four letters:First and Third letters havd harkat known as Pesh
4. A muslim once told me that all muslims can read the scripts(Persian/Arabic etc) even if they don’t understand the language. Was he wrong?
A person knowing Urdu Alphabet can recognise Arabic / Persian Alphabets, but Arabs can not recognise all Urdu letters, as there are more letters in Urdu than Arabic.
