If your black soil came in bags, it probably isn’t very fertile or biologically active. Your manure should be composted before applying. Organic does not mean never using any fertilizers. You can get organic prepared fertilizers, or use lots of good, LIVE compost.

the seeds might be rotting due to the manure manure is better if is applied after seeds have grown a bit or dug in while preparing bed and allowed to degrade, another thing you can do is use a drum with a tap on it and put manure into the drum and fill with water draining some out (via the tap) and mixing with water at rate of 10ml per litre of water (not sure of imperial measurements sorry) and water the garden with it. A really good thing to do is to create a worm farm which will compost plant waste (food and plant cuttings etc) then run water through it doing same as for liquid from manure, then you can use the compost to replenish the soil you could get canteen, teachers and students to put the lunch left overs into special bin to be emptied into it and worms love paper too. as for the iguanas not too sure on best method of keeping them out but as they eat insects that can be pests I wouldn’t be worried about them myself, here in Australia we love seeing reptiles in our gardens ( other than snakes of course lol).

I can’t help with the iguanas. Could it be they are eating the seeds or sprouts. I have rabbit trouble and finally had to fence my garden–I used rabbit wire and metal posts and some pieces of wire to hold the fencing to the post. I know our school doesn’t let the metal fence posts for safety reasons. . . . any way, look at the kind of plants you are choosing–bush green beans, snow peas, lettuce, swiss chard , radish are easy to germinate and grow and grow fast as are zinnias, bachelor buttons and nasturtiums. It sound like you have enough sunshine–veggies like full sun., but afternoon sun is good. Cucumbers and zucinni are easy to grow, too, but take up a lot of room. I guess you could devote one of your beds to viney plants. I’d also recommend mixing your soils and manure together and maybe mix in a bag or play sand to lighten it up. Make a row with your finger or stick and put the seeds in–3 at a time–one for the crow, one for something and one for me! then sprinkle just a little bit of soil over the seeds. Once all the seeds are in, water well with a fine mist. I know it’s hard to cultivate at school. I used a claw to mix up our soil and a little rake to smooth out the clumps. You cannot let the seeds dry out until they have germinated and are a few inches tall so that means sometimes daily watering and I know that’s hard at school. Good luck–maybe it’s just a flukey year for gardening where you are. Make sure you buy good seeds–I like Ferry-Morse.

Manure is fine (so long as it is not fresh out of the butt) and has been used for years and years. It should have been worked into the soil before you planted anything as the roots are the only part of the plant that will benefit from fertilizer.
Some plants refuse to sprout because either the soil is too cold where they are planted or they are duds. That is why we plant more than one seed.
High heat will slow a garden down @90F it stops growing so maybe a partial shade wall like a trellis on the south side might cool the garden enough and give it enough light . Mind you, many plants do not need direct sunlight to grow. Look at your dandelions. They grow eveywhere.
Iguanas? fence or dog or both.

Look for natural and organic alternatives to chemical fertilizers, such as the use of compost. Natural fertilizers, compost and organic materials encourage native earthworms. The soil’s organic matter contributes to good soil structure, and water-holding capacity. Improve the soil with organic matter and fertilizers to develop the best soil for growing seeds and plants.

Organic Gardening Tips -

Your main concern when organic gardening is soil health. You want your little ecosystem to be as strong and healthy as possible to support the plants you’re growing and the beneficial microorganisms within the soil that depend upon your plant’s byproducts for nourishment. As you know, these elements work symbiotically to create the best environment for all to survive. Most gardeners begin with a test kit that will provide a detailed analysis of the nutrients present, as well as the acidic or alkaline reading and the drainage level.

More on Organic Gardening -

This should be of help to you with more advice on that.