Since no one has replied, I will attempt to answer your questions...anyone please feel free to correct me if its misleading or incorrect!!
1. Studio flat/1-BHK per month ( in areas upto 1 hr bus travel distance from Dubai Internet City?) having A/C and washing machine in it. Please mention those area names too.
Firstly, not sure if you want to catch the bus. Probably more convenient to rent a car. The main areas around DIC that have apartments are Marina, Greens, Gardens. Studios are around 60-70k, 1Br around 90-110K. They will all have AC & all white goods (fridge/washer/cooker). If you want to go a bit cheaper, try Bur Dubai, Karama, Satwa, Deira. 1brs are around 70k. But the commute is slightly longer and you'll be in traffic most of the time (plus you will be hit with the SALIK tag fee at Interchange 4 of 4AED per crossing - so thats 8 AED as its 2 crossings a day). But normally still within the 1 hr timeframe on most days. Sharjah will be even cheaper but this is outside of the 1hr timeframe (more like closer to 2 hrs). Bus times, or stops or routers - I have no idea.
2. Advance rent of how many months to be paid to landlord? When is it refundable?
1 year in advance. Some will ask for it all in 1 cheque, others allow 2 or 3 post dated cheques. Its not refundable of course as its your rent!
3. What are costs of water,electricity, air-conditioning and normal Internet usage per month?
We bundle our TV & Internet with du, its around 350AED per month (we have a 2MB connection).
Water & Eletricity for you on a studio/1br will probably be around 400-600 AED per month.
4. Travel costs by public transport per month? Also provide leads for what types of transport and which are available and good and economical currently?
Never taken the bus so won't know. But you can rent a car for a month for around 1,300-1,500 AED, maybe less depending on the car.
5. Is it mandatory to approach a rental agent to book the flat or can we directly go to landlord? What will be agents fee?
Don't have to go to a rental agent. Check out the listings on gulfnews.com or dubizzle.com or even in this forum and some listings may come directly from the landlord. The agent's fee is 5%. Obviously better if you can avoid this fee!
6. What will be cost of vegetarian food+breakfast if we plan to eat outside?
Eating out is generally cost effective, there are plenty of vegetarian options and outlets. A meal for your family can cost as little as 20-40AED depending on where you go.
7a. How much it costs if we cook at home?
This depends on how much you want to buy and where you buy it from. You can stock up cheaply at places like Carrefour or Choithrams. Probably works out the same or slightly cheaper than eating out. Of course, this is probably much healthier than eating out!
7b. Cost of buying utensils for cooking there( for South Indian food)? Electric Cooker etc..
This is all quite cheap - probably at Carrefour or
Ikea you can get all your kitchen utensils, pots, cookers etc for less than 500 AED. Of course you can also get second hand which will be cheaper.
8. What will be the cost of cellphone prepaid cards per month? Do cellphones purchased in India(Nokia make) work there or do we need to buy new.
Your phone will probably work with the UAE SIM Cards. You can get prepaid cards in 25AED or 40AED. Not sure what the call rates are so can't advise on that. If you need to buy a phone, you can get relatievly cheap ones here or second hand.
9. Cost of TV,DVD player and Cable TV bill per month? How is the resale values for these?
Depends what you want. As mentioned in (3) above, we bundle our Cable & Internet with du (also known as DIC) and its about 350 AED a month. Im not sure of the prices, maybe check out carrefouruae.com? Resale, Im not sure. Best way to know is to check out the listings in this forum (For Sale section) or other classifieds such as gulfnews or dubizzle.
Hope this helps & good luck