When insecticides are on the ground do they get taken up by the roots and end up in the fruit?
Each product will have a description that indicates whether or not it is systemic or contact only. Check the packaging.
A “systemic” pesticide circulates within a plant for a period of time. Depending on the compound and dosage this can be for anywhere from two weeks to 14 months. Also, some are applied foliar for uptake by leaves and some have instructions for soil drench for uptake by roots, and others have instructions for either.
Systemics are not limited to insecticides - there are also fungicides and virucides.
Whether or not a systemic contains substances harmful to other organisms is dependent on the product.
There are also non-systemic pesticides which nonetheless contain mineral(s) or other compound(s) that plants can inadvertently uptake and eventually end up in one or more parts of plants. This is the legacy of organo-phosphate pesticides and a few other types.
Not all pesticides are poisons. Some are bacteria spores that destroy the pest or disease. Others are mechanical - they entangle weak insects with a sticky substance. A few more are barriers - they encase the fruit in silica.
Insecticides are not all systemic. Issue with some is even though they are not systemic they may not be worth buying because they are so weak. I bought neem oil to control aphids. I still have neem oil in the garage from two+ years ago because it is so ineffective. Makes you wonder if some of these products go bad and should just be thrown away. I would say on the flip side you don’t want to poison yourself. If you want my opinion fruit trees are going to be pretty hard to grow without a insecticide for the most part. I have disease free plants unsprayed like my Seckle pear because they are so disease resistant but I have had to take out plants this year because I got them from the nursery and they were not sprayed. I think the medium is during Christmas and right before the leaf break happens spray dormant spray on it. I learned the hard way even trees coming from the nursery can have serious problems if left unsprayed. A can of bonide dormant spray is 12 dollars on Amazon and you can buy more than one for free shipping. Dormant spray is still considered organic too. Many think organic means no sprays but all organic means is it is derived from materials on earth. There are sprays many consider organic like dormant spray, captain jacks and copper spray. If you don’t spray it is kind of foolish assuming you are growing fruit trees. If you are growing cheap annuals I find very little reason to spray. Spraying something like a squash will take away any cost saving from the store.
Neem only works when minimally processed. And storing it without temp control damages effectiveness.