what actually i have to do with the assignments and puzzles ?
Assignment and puzzles
you have to solve them 
they are important to understand working of code for beginners
practice coding on cb ide is necessary or we can practice it on other ide too ?
practice on ide is preffered
but you can use any one
you can also use offline ide install in you machine as well
its your choice
will practicing on other offline ide affects on my progress report? and are my doubts visible to TA only or too many people
NO
you have to submit code at question in your course
only then you progress will increase
before asking doubt to tas you can paste you code at
click on file->save->link will be generated
send the link of code generated
it will look like https://ide.codingblocks.com/s/nos
and share generated link