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There should be not issue in amending the soil to increase drainage and overall condition of your garden soil.
Here are a few links for you with more information.
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/how-to-improve-clay-soil.htm
https://www.gardeningknowhow.com/special/organic/how-to-easily-improve-your-clay-soil.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/improving-garden-soil.htm
https://www.gardeningknowhow.com/edible/vegetables/vgen/vegetable-garden-soil.htm

if you cut off the spent flowers of the Iris it helps strengthen the whole plant by not having to use all of their energy on making seed....many flowering plants need deadheading...it usually will not stop the flowers blooming next year.....b

Sow at the beginning of your growing season or as directed on the seed package. Sowing now might work because of the recent rains.

Choose a wildflower seed mix that contains native plants adapted to your dry climate so it will thrive without much watering. You will still need to water enough to keep the soil moist during the seed's germination period (usually requires between 1 and 4 weeks). I would recommend removing the grass before starting if you want even establishment of the wildflowers; otherwise you might have a lower number of plants becoming established. Also, place a sheet or row cover over the germinating seeds for the first 7-10 days to keep them moist.

These articles provide some ideas:

https://www.gardeningknowhow.com/ornamental/flowers/fgen/planting-wildflowers.htm

https://www.gardeningknowhow.com/special/spaces/a-wildflower-garden-in-your-backyard.htm

This depends on the species, whether the plant is an annual or perennial, etc. For seedlings that you have started indoors, here's how to decide:

https://www.gardeningknowhow.com/garden-how-to/seeds/when-to-transplant-a-seedling-plant-into-the-garden.htm

After the foliage of day lilies, gladiolus, and coneflower turns yellow or brown, you can cut it back. Or you can wait till spring to remove the dead leaves.

If you are in a cold region, gladiolus bulbs should be dug up for the winter. Here's how:
https://www.gardeningknowhow.com/ornamental/bulbs/gladiola/storing-gladiola-corms.htm

This article explains how to remove an entire yucca plant:

https://www.gardeningknowhow.com/ornamental/foliage/yucca/removing-yucca.htm

If instead you just want to remove some roots, you can try to cut off the invasive roots from the main plant by plunging a sharp shovel into the ground. Then install a root barrier.

Unfortunately we are not able to recommend specific products, but pH tests intended for garden soil are available at many hardware stores, garden stores, and online gardening retailers. Some of the very low priced options may not work well, but you can always test the one you choose on samples of vinegar, etc. to check accuracy.