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Thistle, mallow and maybe another I'm not sure about.

It is doubtful that they will grow under the footing of a block wall. It's more likely that they will spread by wind blown seed. Keep an eye on your side of the wall for young weed growth, and dig or pull before they mature and go to seed in your yard.

If you have property owner permission on the other side where your husband cut, and you are competent with safe and effective use of pesticides, then you can use an "organic" or chemical herbicide (weed killer), general purpose or selective for "broadleaf" weeds.

http://www.saferbrand.com/safer-brand-fast-acting-weed-and-grass-killer-rtu-32-oz-5055-6

I think you may be referencing Sandburs.
This article will help you.
https://www.gardeningknowhow.com/plant-problems/weeds/controlling-sandbur-weeds.htm

A little research shows that a deficiency of available phosphorus will encourage Canadian thistles.
Here's a good article for you: https://www.gardeningknowhow.com/plant-problems/weeds/canada-thistle-control.htm

Make sure to follow all advice and recommended use for the product that will be found on the product label.

Additionally, certain areas have different procedures on when and how you can apply. Here is an article to help you find the local extension service nearest to you, as they can help you with local regulation:

https://www.gardeningknowhow.com/extension-search

Here is an article that will explain more on correct use of the product, and link you to fact sheets and more:

https://www.gardeningknowhow.com/plant-problems/weeds/glyphosate-information.htm

This is quite odd. They will require alternating cool and warm periods to germinate, though this could have been done prior to your receiving the seeds.

They like to be direct sown, since they grow a taproot. Plants with taproots to do not well when transplanted. You will likely see growth through the winter, but their best look will be achieved next year.

Here is an article that will help you to grow these care-free plants:

https://www.gardeningknowhow.com/ornamental/flowers/sea-holly/sea-holly-flowers.htm

It sounds like thick soil has lead to overwatering. Generally, I wouldn't water these drought tolerant plants at all! They are well adapted to dry conditions, and will not thrive in wet soils.

Make sure to check the soil with a meter. Make sure that it is dry, down to about 3 or 4 inches, thoroughly. Once it is dry down to this depth, you can water enough to keep your other plants happy.

This article will help you to use a soil moisture meter:

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-moisture-in-plants.htm

This article will help you to grow globe thistle:

https://www.gardeningknowhow.com/ornamental/flowers/globe-thistle/growing-globe-thistle-plants.htm