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Unfortunately there is no transit visa on arrival at Dubai airport for Indian passport holders. You need to get the visa beforehand. So you can apply through Emirates website where it costs 25 USD or you have to apply through the VFS DUBAI VISA PROCESSING CENTRE (DVPC) - here also there is service charge but its only Rs 820. Check out http://www.dubaivisa.net/india/duration48hours.html
I just returned from my trip a few days ago and also had a long layover in Dubai and got my visa through Emirates.com. Its more expensive, but was convenient as the whole application procedure was online and did not have to waste a day going to the VFS office. So please clarify your visa situation first.
Regarding your 1st question, I think one hour would be very tight to catch the metro. Consider the following factors
Hope this helps.