As usual VaultHunter101 covered all the details.
My commentary from when I was in your position is that it’s fairly easy to get the hang of the fight. You’ll probably die the first 2-3 times you try it, but then you’ll know what Pete’s nova signal looks like and have a pretty good idea of timing. I just kite him around the room, making a point of being next to the scaffolding when it’s nova time. Sometimes this means one doesn’t do the full circle of the room (cutting across the middle because you know you’re low on time); sometimes it means dancing back and forth around the scaffolding because you got there a bit too soon.
Even once I had the fight figured out, perfect runs were rare. Getting hit by a nova once or twice isn’t the end of the world, just summon the spiderants and clear the DoT and try to get back into the rhythm of the fight.
Gear - in my experience neither the Trespasser nor the Flying prefix on the shock Sandhawk are necessary for Maya. I used a few Storm Fronts to start the fight. Pete’s slow so he stays in their area for quite a while.
Using the shock Sandhawk, Bee, and Legendary Cat (all level 72 - I did my Pete farming before ever visiting the Peak), I could reliably break his shield at about the time he does his first nova. That’s important because breaking the shield also triggers him to nova, so you need to be able to duck back into cover. Once the shield is down, you’ll knock his helmet off almost immediately and the rest of the fight should be pretty easy.
Never. Reset if you want to, but it’s not required. Handsome_Dad has a post about Maya clearing the Peak using only easily farmed gear like the Lyuda, Hornet, etc. What I’m doing (very slowly) is using a few quest rewards like the Pimpernel to start off, and transitioning to something like a Lady Fist and Lyuda setup once the Pimp doesn’t get the job done anymore. Which could be now (OP4); I’m not exactly putting a lot of effort into the Peak climb.
Killing Pete roughly ten times so that you can buy a seraph item will definitely help if you’re stuck. An OP3 Antagonist made a big difference back when my Maya did the OP3 to 4 Peak run.