We have been gifted a natural paper rope Moses basket. It has a sturdy base, firm fitting mattress etc, but we aren’t sure about the breathability on the sides. How can we check this/ ensure it’s suitable for our newborn? Happy to provide the brand if required.

There are no mandatory standards for bassinets in Australia.
Product Safety Australia does have some recommendations (Buying Tips) for bassinets which include:

Ensure the sides of the bassinette are at least 300 mm higher than the top of the mattress base.
Ensure it has a wide stable base and a sturdy bottom so that it won’t tip over.
Ensure the mattress fits well and is firm, smooth and no more than 75 mm thick.
If the product has folding legs, make sure it cannot accidentally fold during use.
https://www.productsafety.gov.au/products/babies-kids/kids-furniture/bassinettes

Are there any potential hazards such as entrapment, strangulation, suffocation or fall risks associated with using this product?

As with all bassinets, once baby is attempting to roll, they need to be moved to a cot.
Have a look at Red Nose information on bassinets
https://rednose.org.au/article/bassinets

Second hand furniture
https://rednose.org.au/article/second-hand-nursery-furniture