I briefly mained ZSS a while back so I thought I'd speak up.
To add to what's already been said about neutral...
Do not challenge her short hop aerials with aerials of your own. ZSS' Nair confirms into a ton of follow-ups and it just isn't worth the risk. Similarly, don't challenge bair at mid to high percent if you can help it because that can also kill you surprisingly early which will make this matchup extremely hard to win. Also be aware of the utilt in neutral because that can start a combo too. Her jab is also a frame 1 move.
I've also realized the N-air and flamethrower can destroy this with careful timing allowing two moves you can use to both destroy the projectile and give some free damage on ZZS, risky though.
You have to hit the paralyzer shot tail first if you want to use nair. It's really, really particular spacing. I do kind of disagree about shielding the paralyzer though.
If you dash at ZSS and powershield it, you'll slide a little too which should put you in range for a quick punish (jabs, dtilt, maybe even a grab). This is worth going for a power shield every time you're in range to punish off of it imo.
Also, If you don't powershield, be really careful about your OoS option and you shouldn't have too much trouble. Don't roll. Spot dodge if ZSS comes in for a grab after the paralyzer (this is very possible! just hard when she's close since her grab is 14 frames) and go for retreating flamethrower if ZSS approaches with SH aerials instead. Don't use flamethrower too long though because that's a free flipkick once ZSS is out of hitstun. ZSS can also mix up with full hop aerials which could be a problem if you are already committed to neutral B. If she hesitates after paralyzer is shielded, drop shield and reset the situation.
You are in for a lot of damage if you get hit by it so I can see why you might want to avoid the paralyzer altogether. The game can also be won and lost by spot dodging grabs in neutral so I'd say that while it can be risky, its one of the few ways us Zards can turn the tide in our favor.
Flipkick. I've actually found it easier to take some damage and jump into the strait dunk while you're at low %.
That's an interesting option. I've always tried to utilt her out of it. Seems safer to me. It's harder to do when she comes in for the side kick rather than the dunk/bury but it works.
Don't try to inturrupt this move with usmash though. Your character is lighter when charging a smash attack so you might just lose the stock if you mistime it. Plus it doesn't reach nearly as high as utilt.
Otherwise, look out if ZZS throws you backwards, if you DI towards her, that's a free flip kick, if it's off stage, that's a dunk
This cannot be stressed enough. If ZSS takes stocks even a little early, the match becomes so much harder for zard. You have to DI these correctly to have so much as a hope for this matchup. We feed off of rage in this matchup extra hard.
On the subject of getting combo'd though...
Get to the ledge or get around her follow-ups with your jumps. Landing with nair is not too great because ZSS' side special and usmash will outrange it no matter how you try to land with it.
If you get boost kicked at the end of the combo, smash DI it and then try to get out on the last hit. Otherwise DI the hit down and towards the stage because chances are its sending you straight to the corner blast zone.
And ledge trumps...
Grabbing the ledge with flare blitz can be useful if you think there's a chance she tries to trump you (immediately inputting a getup option works too). ZSS would be nuts to risk getting hit with that. It is important to note that regrabbing the ledge with flare blitz
will not refresh your invincibility. Also try to avoid regrabbing the ledge in general since ZSS can combo dsmash into flip kick spike off of it and ledge regrabbing is a great setup for that kill combo. Not so great for zards though.
Rock smash/hurl may be your best bet to get around the bair after the trump but this can be baited so its a 50/50. It also stalls your momentum if you're still rising so inputting your second jump first will allow you to keep your options open afterward (that whole last paragraph is theorycraft though).
Offensively, Zard is pretty limited and is forced to play a much more reactive play style. Flamethrower isn't very safe. Losing a nair to nair clash spells a lot of trouble and zair will catch repeated aerial approaches (nair and fair). Combo throws are combo throws. You better not whiff a dash grab though. Our edge guarding is a lot harder because ZSS has flip kick and a second jump. Reading her recovery is hard but if you can do it, you will rack up percent a ton easier. It's worth trying to bait the jumps with empty hops to help; both offstage and when ZSS is trying to land. ZSS' initial dash is also pretty long, if you can read that and use it to your advantage. In terms of landing kills, I would not recommend the hardest of hard reads unless it's a last resort (ZSS is up a stock and has 50 on you). Jab 2 to grab and Jab 2 to fly are extremely good and reliable. Use those first. I'm not sure if she can mash out of the frame trap with flip kick though.
You pretty much have to be on tilt the whole match watching out for grabs, nairs, and paralyzers to avoid combos like the plague. ZSS also has a ton of kill options, some of which are available well before what Zards would call an acceptable kill percent in this matchup. You can't mess up. She has way more room for error. Easily 7:3, possible 8:2 if ZSS has solid matchup knowledge. Not necessarily unwinnable but you would need to play extremely well.