Hindi - changing from Aap to Tum

Where is "tum" used and where "aap", to mean "you"? Can "tum" ever be used towards people older than yourself? Have you ever switched from using the "Aap" form to using the "Tum" form as the relationship with another person became less formal?

"Tum" तुम is used for people younger than or equal to the age of the speaker. "Aap" आप is used for people of older age, or even for people with equal or younger age when one wants to show respect/reverence/affection. For example, a mother can say "aap" to her small kid also with love. But these are informal instances. 

Changing from "aap" to "tum" as the relationship goes more informal, can also happen at times when used for people with almost equal age or status... It is possible and happens at times.

Hindi: chuuRiyaaN चूड़ियाँ in a screw

What is meant by the word chuuRiyaaN which is the spiral-like carving around a screw... I can't remember how it is called in English...

It is "thread" in English. You are right that churiyan is also used for threads of a screw or of a machine, apart from its usual meaning of "bangles". 

http://en.wikipedia.org/wiki/Screw_thread 

"A screw thread, often shortened to thread, is a helical structure used to convert between rotational and linear movement or force. A screw thread is a ridge wrapped around a cylinder or cone in the form of a helix, with the former being called a straight thread and the latter called a tapered thread."

Hindi: As if that weren't enough

How can one say in Hindi this phrase? "As if that weren't enough"?

One can say, "Jaise ki ye ye kafi nahi tha" or "Mano yah paryapt nahi tha"

 जैसे कि ये काफी नहीं था / मानो यह पर्याप्त नहीं था

Hindi: work stoppage

The Hindi word for this is generally written as "bandh" in English contexts. But is it written as "bandh" in Hindi/Devanagari or as "band"?

In Hindi/Devnagri it is written as "band" बंद and not as "bandh" बंध .

Hindi: pasand hona vs pasand karna

"mujhe yah kamiiz pasand hai" Vs "maiN yah kamiiz pasand kartaa hooN", which one is more common or correct? 

Both are equally valid and used commonly. My personal choice to speak would be the later one, but it depends on personal choice and both are used popularly.

 

Hindi: Rann of Kutch

How is Rann of Kutch written in devnagari?

It is written as "कच्छ का रण"

Hindi: xyz ke chalte

I notice people using this peculiar construction: "विरोधियों की मुहिम के चलते बसपा को दोगुना चंदा" (virodhiyoN kii muhim ke chalte baspaa ko dogunaa chandaa) instead of the normal "विरोधियों की मुहिम के दौरान​ बसपा को दोगुना चंदा". I first noticed it on TV news segments on YouTube and it seems to be used more in headlines. Is this correct in Hindi?

If the meaning intended was "during", then the first sentence is incorrect because it means "due to". 

"विरोधियों की मुहिम के चलते बसपा को दोगुना चंदा" => "Due to"

"विरोधियों की मुहिम के दौरान​ बसपा को दोगुना चंदा" => "During"

Sanskrit: परमात्मा

I heard the expression (paramatma) in a mantra by Deva Premal and my impression was she was pronouncing it more like "paramatama" (with an "a" or maybe just a shwa between t and m). I was wondering if this was the usual way you pronounce it or was it just due to keeping up with the melody? 

My personal take is that it should be like "aatmaa" आत्मा and not "aatamaa" आतमा , means there should not be "a" in between or full pronounced "ta" त . It is half त्