Hi and welcome to the Forum! Big welcome to another Ohio gardener!
There seem to be a bunch of different questions mingled in there. I'll try to sort them out and answer some and maybe other people will jump in.
"Cucumbers do well through May and then all the vines die off. Tomatoes roots also get ruined by middle June. Same for squash, lettuce, and melons and cantelope. " The cucumbers, squash, melons and cantalopes are all in the same family, known as cucurbitae. As such they are all prey to the same pest known as squash vine borer or zucchini root borer. It's a menace! I can have nice big healthy zucchini vines with beautiful yellow flowers on them and practically over night they have wilted to nothing. That's the squash vine borer. Type one of the names into the Search the Forum feature and you will find lots written about them and what to do about them.
The squash vine borer should not be responsible for damage to the tomatoes or lettuce. I've never had much trouble with pests and tomatoes. What does the damage look like? If the roots have turned black and mushy, that is root rot, which is a fungal condition that results from over-watering, poor drainage and the roots staying too wet. If the roots have lots of round lumps all over them, that's probably a root knot nematode, a little worm that lives in the soil and infects the roots. Don't know anything about what's going on with your lettuce without more descriptions.
You said your garden is all organic and then you asked about what fertilizer to put down and how much. That sounds like you are asking about synthetic fertilizers, which would not be organic. For organic gardeners the best thing would be compost, well aged composted manure, and whatever other organic materials you have around -- leaves, sawdust, coffee grounds, etc. There are commercial organic fertilizers with ingredients like kelp, bone meal, blood meal, fish emulsion, etc. The package would tell you spreading rates. When using compost, quantities don't need to be precise, use whatever you have, you can't over do it.