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Rosemary needs a light, good quality potting soil.
Your mixture is likely way to heavy and your plant will not do well.

https://www.gardeningknowhow.com/edible/herbs/rosemary/rosemary-grown-in-containers.htm

Rosemary is tougher than other woody herbs, so you can hard prune it and it will come back looking better than ever. However, it is best to wait till winter for drastic pruning. You can cut 1/3 right now if you can't wait; then another 1/3 in late winter.

Here's how:
https://www.gardeningknowhow.com/edible/herbs/rosemary/rejuvenation-of-rosemary.htm

https://www.gardeningknowhow.com/edible/herbs/rosemary/pruning-rosemary.htm

Normally ants are after honeydew, which is secreted by pests such as aphids. Here is more information and how to control them, as well as diseases of rosemary.

https://www.gardeningknowhow.com/plant-problems/pests/insects/controlling-aphids-and-ants.htm

https://plantvillage.psu.edu/topics/rosemary/infos

I'm afraid that the clay soil the plant is in will not be very suitable for a container application. It has a tendency to stay, either, too moist or too dry. This can lead to fungal infections resembling what you are seeing on your plant.

You will need to change the soil to a suitable potting soil, or at least add compost to the clay. I do not recommend the latter, as using clay soils in containers is quite a chore.

Once you get it into a suitable soil, then you can begin treatment. This will be a fungicide.

These articles will help: https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm

https://www.gardeningknowhow.com/edible/herbs/rosemary/rosemary-grown-in-containers.htm

They require water when they start to dry out down to an inch or so. There is no set time, since this depends on the conditions around them. Overwatering will lead to rot, and underwatering will lead to a failed cutting. In this case, though, underwatering is better. USUALLY, you will not need to water them at all until after you remove them from where they are rooting, as the humidity should remain high enough to prevent severe evaporation.

They will want to remain in temperatures that don't exceed the 80's during the day, and does not fall below 50 at night for proper rooting. A seedling heat mat can help if the temperatures cannot remain as warm as you need them.

This article will offer more information: https://www.gardeningknowhow.com/edible/herbs/rosemary/how-to-propagate-a-rosemary-plant.htm

Usually, this can take anywhere from 1 week to 3, depending on proper conditions around the cutting. Using rooting hormone will make this faster. Any nutrients in the soil will hinder the process, so a soiless mix like Peat moss or seedling mixes will be best.