I've had them for a month from a reputable vendor and they have blooms on them but they are now looking like they're developing mould on their leaves. What can I do about this please? They are still quite small.
Likely this is Powdery Mildew, which is a very common issue in gardens.
Here are some links for you.
https://www.gardeningknowhow.com/ornamental/flowers/achimenes/grow-achimenes-magic-flowers.htm
https://www.gardeningknowhow.com/plant-problems/disease/powdery-mildew-homemade-and-organic-remedies.htm
Damage on the leaves of my achemines is a strange puzzle-ing look. No holes, but coloring from the leaf seems to be missing. I have looked with a magnifying glass and see no bugs. Any idea?
Many pests are so small that you cannot see them.
Treat your plant with Neem Oil.
Neem Oil is organic and safe for people, pets and bees.
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm