What are some Indian traditions that have scientific reasoning behind them?

The other source for such reasons is that people generally try to bind rationality to actions which are based on an archaic thought process. The reasons were re-searched and later added to the rituals to give them some rational validity. 

Yes, there are some arguments which are true especially regarding medicinal uses of neem, turmeric etc. But, can you call penicillin an outcome of the culture of Scotland? Penicillin like other group of medicines are an outcome of research of people living in their respective countries. Same is the case with neem. It is just another pebble we collected in our pursuit of knowledge.

Let's look at the case of trimming nails or using needles at night. Are we stupid enough to trim nails at night when there is no light. First,we'll injure our fingers, foot would come next. It is not a legend as such. It is common sense. Same as you don't colour a painting in pitch dark room. Now, why should I not cut my nails in the night when their is a glowing bulb on my wall? 

The one notion present in many of them is some intangible "positive energy". What the hell is this positive energy? Every type of energy in this world is both positive and negative.

• Heat gives you warmth but can burn you.
• Light gives you ability to see but can blind you.
• Nuclear energy can give you power but can kill you.

Let's take some of them.

• Eating with your hands improve digestion and engage you senses. It has never been proved. There are 101 better ways to improve digestion. Drink plenty of water, take a walk half an hour after you eat and don't include a lot of spices in your food. The eyes are enough to tell your brain that you are eating. We don't need a complex system of hand to brain nerves to solve that.
• Celebration of Holi. So, they created a whole legend out of it to kill mosquitoes, to kill mosquitoes "for one day". I have seen enough of Holika Dahans. The mosquitoes don't wait another hour to come back.
• Keeping women away from temples and kitchen so that they take proper rest and so as to take care of certain kind of cleanliness. First of all, menstrual flow is not dirty. Most of it is simple blood. As far as rest is concerned, she can be a relay racer, not just inside any temple premises.They are not allowed even in simple prayers at home which involves two steps to a different room. Please, read Quora User answer. It is a very good example of absolutely false perceptions from the first line.
• Yajna is organized to do some intangible purification and killing insects.So, they do an entire process of several hours singing several hundred chants to kill some insects, just for a couple of hours. In fact, after a yajna procession, you'll see a lot more insects coming on the leftover fruits and other paraphernalia. It is also a source of air pollution and wastage of wood.
• Doing a namaskar simulate some pressure points. Again, never proved and not going to be proved in another 1000 years.
• Women ornaments(Toe rings, and bindi or vermilion between eyebrows is usually worn by married women because these ornaments press against the points related to sexual and reproductive organs). I mean, seriously! What reproductive organ grows out of your forehead. If there is any "pressure point" for the reproductive organs, I guess, we all know where they are.
• Halal meat gives the animal minimal amount of pain, do some intangible cleansing and pour all the blood out. How can beheading in a straight shot give more amount of pain to the deceased animal? Can you voluntarily sneak out some blood from your body or is it an involuntary action? And for heaven's sake hookworms don't travel in your veins.
• Drinking water with hands. Another false perception for digestion. No salivary glands get activated specially on the touch of water to your hand. People drink water with hands as they have no containers to fill the water. Simple. Isn't it?
• Wearing dhoti. People wore dhoti because they never had the concept or the talent of stitching. Even cotton pants can be washed regularly. Is it Rocket science, fellas? Wearing pants is not greed and it is not going to stop you from eternal bliss. It might stop you from dying from cold in Canada. If we go according to Baba Whatever Ji Maharaj, we might have to live our lives in undergarments.
• Ancient form of Indian punishment. A doctor who was an MDS (Master in Dental Surgery) performed an experiment regarding activities in brain after an ancient exercise which involved squats was performed. He found out that the the alpha waves increased drastically after the exercise was performed. Alpha waves is a state of quiet and resting alertness and it also indicates relaxation. So, they found out that during the exercise you are concentrated and after the exercise you are relaxed. It is simply awesome. Suddenly, I am feeling more enlightened. Are you feeling the same?
• The elders rotate salt and lemon because when revolved around, it would kill all the bacteria around the person. It forms an aura layer of antibiotics around the person. Not only has this, revolving around the person balance the magnetic field too. So, the person would sit all day, at the same spot, smelling a lemon which was revolved a couple of times and has formed a layer of antibiotics to kill all the evil bacteria's around. These things are getting worse man. Antibiotics are effective when we eat them, that's the whole difference between antibiotics and disinfectants.