Temporary employees in the public sector generally can't join the superannuation scheme (they can buy back their temporary service if they become permanent employees). Public sector employees now pay A1 PRSI contributions (towards state pension at retirement among other benefits) and that applies whether you're permanent or temporary.
Yes, you can join a union.
Yes, you can join a private health scheme. No, public sector don't contribute towards private health (not in my experience!) however they may facilitate deductions from salary to pay for it and you would most likely be considered part of a group scheme so would be eligible for 10% reduction from the healthcare insurer.