1 - If I am not mistaken, you have received an invitation from NSW (not DHA / SkillSelect) to apply for NSW state nomination (this is colloquially referred to as a 'pre-invite' on this forum).
You have 14 days to do this.
If NSW decides to invite you, then you get the DHA / SkillSelect invitation to apply where based on current policy you have 60 days to lodge a visa application.
2 - A bird in hand is worth two in the bush is my mantra - so I would most definitely not let this 'pre-invite' go. I would pay the $300 and apply for NSW nomination.
Then wait simultaneously for a 189 invite come 11 May.
If for some reason the 189 invite rounds become incredibly small - at least you have the NSW application moving along. If you do get the 189 invite, the $300 will seem like a small amount for hedging against the risk of not getting a 189 invite.
3 - Since they are seperate EOI's they should not affect each other, so you would still be able to receive a 189 invite even with the other EOI being assessed by NSW.
190 ACT | ANZSCO 411711 | 75+5
ACWA skills assessment completed 15 Jun 18
ACT nomination lodged 20 Jun 18
ACT nomination 21 Aug 18
190 lodged 21 Aug 18
Added de facto via Form 1436 12 Nov 18
De facto added by CO 14 Nov 18
CO contact de facto medical/functional english 1 Dec 18
Responded to CO 6 Dec 18
CO contact de facto functional english (already provided) 22 Feb 19
Responded to CO 25 Feb 19
Grant 4 Mar 19
Happy to share my experience with ACWA, ACT, SG PCC, Form 1436.