Throne of Glass question

I read Assassin's Blade before Queen of Shadows, right after Heir of Fire. I loved reading it then because it added and air of mystery to Celaena's backstory, but it is really necessary to read it before Queen of Shadows. I also did the tandem read and although it looks intimidating, it made it so much better to read. I can't imagine finishing Empire of Storms and then having to sit through all of Tower of Dawn before Kingdom of Ash. Highly recommend the tandem read and no not read Assassin's Blade before Throne of Glass.

I read Assassins blade after, I don't think it was released yet when I originally started the series. I think that because most of the actual world building occurs in the main series, Assassin's Blade relies on you to lean on that at least a little to have more understanding of the characters and what is going on. Beyond that, I would say to still read Assassins blade earlier on in the series (After Heir of Fire at the latest) but I think going into the books without context of Assassins Blade made specific parts especially impactful.

I definitly did not tandem read. I had a really hard time reading Tower of Dawn. I mostly skimmed it. I couldn't get into it and really only needed the plot so I wouldn't be lost when I read the next book (I read Empire of Storms before Tower of Dawn). There was a couple times in Kingdom of Ash where I referenced Tower of Dawn because I hadn't been enthralled enough to recall details. I don't think this impacted much of my experience besides how smoothly I was able to recall previous events.

I also read Assassin's Blade after Throne of Glass, and that's also because it hadn't come out yet when I started the series.

I read Tower of Dawn after Empire of Storms as well, but looking back I would've rather switched them. Empire of Storms ended in such a way that I couldn't stop thinking about it and the characters throughout Tower of Dawn, and that resulted in me not being that interested in Tower of Dawn.
When I reread the series I am definitely reading Tower of Dawn, then Empire of Storms and then Kingdom of Ash.