How to extract flavour from fruit without heating it or using alcohol? I am curious to know, how fruit syrups and flavours are made commercially and how we can extract the maximum, true flavour of a juicy fruit (such as oranges or apples) as well as denser and less juicy fruit (such as mangoes and peaches) and also berries at home, so I can use the flavour to make fruit flavouring for tea and other desserts.

The problem I have with simple syrup is, it is far too sweet and ends up with an artificial tasting saccharine flavour. The other problem is, I find cooked fruit makes it more sour and it loses its real fruit flavour, which you then try to compensate for and replace with sugar, making it taste more like fruit flavoured boiled candy. That is why apple pies and applesauce, fruit jams never appeals to me as they taste very fake and sweet.

What I'd really like to avoid is heating it. I can deal with the sugar, as it is usually diluted with other ingredients anyway.

I know you can soak things in alcohol, but the alcohol only disappears if you then cook the final food product. It will remain if I want to use it in non-cooked food, such as add as a syrup to snow cones.

The other way I thought of is to puree the fruit, strain it and am left with the liquid. This would not work for mangoes, peaches and berries which unfortunately, are the fruits I am interested in. I might get a tiny portion of actual liquid from a giant volume of solid fruit. I know that if you suck on a popsicle with only fruit juice, you end up with a block of ice, because you ended up sucking the (concentrated) juice away so all that is left is the water ice. There is a tutorial on Instructables here that reverse engineers and uses this property (of impure water having a lower melting point) to freeze the juice then let it thaw until the juice is liquid but some ice remains, then re-freezing the juice and repeating the process. This is something that can be done at home but I am wondering what other ways there could be that doesn't require constant monitoring and labour intensive.

I say at home, because while factories and shops can get their hands on fruit flavouring and concentrates in bulk, it's hard for a normal person to get it in small quantities. However, surely factories have a way of making the fruit flavouring somehow, because the ice teas, gelato and boiled lollies you buy commercially in general all actually taste like the fruit, and not just of sugar. Wondering how they obtain that flavour and whether we can do that at home, because some of the ice tea that you get in shops actually do taste like real fruit even if you ask for less or no sugar.
Simply, you don't. Your post describes a method which starts with whole fruit, doesn't use heat or alcohol, is achievable in a home kitchen, and has a high yield. Such a method simply doesn't exist. 

Your assumption that "if the food industry does it, I should be able to do it too" is wrong. The food industry doesn't do it. It uses engineered flavors, which create the most salient smell molecules of a given fruit without using the fruit. If these are created using pure chemistry (such as isoamyl acetate for banana flavor), they are called artificial flavors, if they are created biologically (e.g. isolated from mold, as for strawberry flavor), they are called natural or naturally identical flavors. Methods for extracting them from the real fruit exist, but they are too expensive and inconvenient. 

All methods which start with the whole fruit have roughly two steps, first extraction with a solvent and then concentration. The only two solvents usable in your kitchen are alcohol and water (the industry may use others such as CO2, but the technology is not available at home) and you excluded alcohol. As for water, you could in principle do something like a compote or a fruit tea, but as you are looking for high concentration, you are lucky that all the flavor compounds in fruits are already dissolved in water - so your starting point will always be fruit juice. 

By the way, you can probably improve your yield here somewhat with a suitable juicer - a masticating juicer will give you more juice per unit of fruit than a centrifugal juicer. But it will be an incremental improvement, don't expect to get three times as much juice out of the same mango. 

The second step would be the concentration. You are right that heating changes the taste, but that's the only method available in a normal kitchen. The other methods would be freeze drying and vacuum distillation. I haven't heard of even the hardiest food geeks getting freeze drying systems in their laboratories (I wouldn't call their cooking spaces "a kitchen"!), and rotovaps for vaccum distillation are used by maybe a handful of cooks around the world. There, you can assume costs of about 10 000 Euro for the whole setup (including pump etc.) and you need a learning curve. 

And third, if the unchanged taste is so important to you that you decide to pay the 10 000, your yield will still be tiny. It is not just that you get a small amount of fruit juice out of the large amount of whole fruit, you have to still reduce it further to get an actual concentrated extract. There is no way around that, it's simple physics - there is just a small amount of real "flavoring" in each berry or mango, and you can't get our more than there was in the first place! 

If you want to flavor things at home, the most accesible way would be to purchase flavorings used by the food industry. They are rarely available in their pure form, but you can buy flavored concentrates intended for drinkds, such as Tang. Instead of adding water, you can use them to flavor other things like cake glaze or lollies (be mindful of the other ingredients such as sweetener and acid when you do it). 

Another, more expensive option is to purchase freeze dried fruit powder. It does pack a punch of flavor and color, and gives a better flavor than the drink powders. And because it is completely dry, you can use it in places like buttercream where a water- or alcohol-based extract would mess up the texture. They are of course expensive, because of the abovementioned low yield, the industry needs to use kilograms of fruit to produce a few grams of the powder. If you do this, decide if you always need the pure stuff - for the most expensive ones, there are also options of powders which use maltose as the base, giving you more bulk.