Yes, those branching marks are consistent with lens fungus. You may still be able to use the lens: the effect on image quality depends on how much fungus there is and where it is inside the lens. The practical test is to shoot plain subjects at different apertures, focal lengths, and lighting angles to see whether contrast, flare, or visible marks appear.

Fungus can spread, especially in humid storage conditions, though it does not spread extremely fast inside a lens. Because of that risk, it’s wise not to store the lens tightly packed with your other gear.

To slow or stop further growth, store equipment in a dry, well-lit place. Silica gel/desiccant packs can help reduce humidity. UV/light exposure is also commonly used to inhibit fungus growth. Constant humidity encourages it.

If the fungus is advanced, image quality may degrade and internal damage can become permanent. Cleaning/repair may be possible, but whether it is worth doing depends on the lens condition and repair cost.

In short: test the lens, keep it dry, use desiccant, avoid humid storage, and separate it from other gear if possible.