[Thin Lizzy]

Congratulations on your 2 syrians. Like others have said, a big no to sharing a cage or even playing together.
As for the ball, as long as it's cleaned before the other uses it.
Yes all hamsters can get parasites but, this is easily treated when diagnosed.
Be sure to give them a few days to settle and avoid any major cage cleans for at least 3 to 4 weeks doing daily spot checks in their chosen toilet areas. Hams like to mark every bit of their cage.