To observe fasting without taking water is known as 'nirjal upavas' and mostly the followers of 'Sri Chaitanya Mahaprabhu' and staunch Vaishnavites observe such fasting particularly on 'Suddha' and 'Bahula Ekadasi' days i.e the 11th day after 'Amavasya' and after full moon day as per Hindu calendar.
I don't know the exact reason for remaining empty stomach before performing puja, but whatever little I know, I am sharing it. Most of the poojas take long time (few hours) for completion. And according to religious beliefs, the one / couple who sit and perform pooja is not supposed to get up till the end of the pooja. So, I think to avoid urgent nature calls (urination or excretion), it is advised to perform pooja empty stomach. However, they can take simple foods like fruits to withstand.
Secondly when the tummy is stuffed with food items, naturally there will be belching (emission of gas through mouth with sound). Even when someone belches in a high level meeting, they feel sorry / beg for pardon. So, it is not good to emit gases / pungent gases either through mouth or other aperture as it spreads the pungent smell.
During pooja, it would be delightful to have nice fragrance - i.e the fragrance of agarbatti, chandan , camphor etc - spread across as it gives a divine feeling and not the pungent smell.
Please Note: This is what my parents used to tell me. I neither read about this anywhere nor have heard from anyone else other than my parents.
Thanks & Regards