Insecticide and fungicide all in one - is this possible

A lot of fruit trees including apples, blackcurrants etc require a certain number of hours below about 5°C to flower and fruit at their best.
A lot of fruit trees including peaches originate from areas with distinct seasons so they get cold winters and then it's spring followed by a nice hot summer. Not like the UK where the weather yo-yos around all year.
What standard do you require for your peaches?

 

Anything from cats, foxes and soil living critters gets "filtered" through the tree and doesn't affect the fruit at all.
If you are worried about insects you can always wash and peel the fruit.
The sort of things you mention will also be all over anything you buy from the supermarket, greengrocer or farm shop.

 

You won't make any difference to peach leaf curl by spraying it.

There are 2 ways to deal with it:

1 - relax about it - it's unlikely to kill the tree, which often recover by mid summer.

2 - cover the tree between December and April - as mentioned above, the RHS website has a good description of how to do this.

 

If you're concerned that the contents of plant food might be hazardous, it seems unwise to be actually going out and buying poisonous sprays for the garden.

 

That looks like a healthy peach tree - if there are some aphids curling up the leaves at the tips, I'd be tempted to pick those leaves off or spray the aphids off with a water spray, or just wait for some ladybird larvae to arrive...