As far as parallax; underestimate it at your peril.
For an example, I took a brand new shooter out with his very inexpensive new rifle setup (he had no idea what he was buying) that consisted of a hunting package from Savage. Was a pencil barrel 270WSM, plastic stock that weighed absolutely nothing and a 3-9 Nikon scope that was on par with the $49 scopes you see at Walmart. After showing him the basics of getting behind the gun, what's right and wrong, natural POA, rear bag manipulation, how his rifle/upper body/lower body need to be 3 segments of the same 'stick', correcting him as he screwed up he started getting decent groups at 100 yards with it.
Had him shoot some more and he was getting settled in as well as took some velocity readings. I shoot the gun and 2x5 round groups showed it was capable of .75 MOA which surprised the shit out of me.
I decided we were going to challenge him, and the setup and put a 40% IPSC plate out at 550 yards. I had the velocity and bullet information for his factory load and we built a range card for him. He didn't want to shoot first and wanted to watch (think he was a bit overwhelmed and also figured at 9x he wasn't even going to see the target) and I went, getting a 2nd round hit on the plate and handed him the gun.
I got behind the spotting scope and watched as he shot. First shot was 20+ inches low, but chalked it up to him never having shot past 100 yards but he confirmed he had a good shot. Had him shoot again and it was almost in the same spot the 1st shot was, so I called a correction. We came up something like 4.5 MOA and he was right under the target with the 3rd shot. Called another .5MOA and told him to prepare for a hit, and sure enough PING!
Other than him being besides himself, I was amazed as well that this basically bare bones gun even managed to do this.
So where's the part about the parallax, you ask?
Remember how I got a hit, yet someone with a different LOP, cheek position, head position and aspect through the scope than me all of a sudden needed a 4.5MOA adjustment to hit the exact target I just hit with the previous shot?
Parallax
To confirm it, I shot after he made his hit and blew the shot way over the top of the target; I'm willing to bet it was somewhere in the neighborhood of 4.5MOA.
As far as parallax/mirage, look at the reticle, NOT the target. If the reticle is bowing/bending at the corners, there's parallax. This will be the indicator with or without mirage.
