Incredible deal opportunity, nervous because it’s over my budget

You asked what you need to know rather than whether to do it, so I'll answer that literally. I'm a contractor, so I'm the guy who eventually writes these numbers, and there are four things in your post I'd want answered before your inspection period closes.

THE POOL IS THE BIGGEST ITEM IN YOUR POST AND YOU GAVE IT SIX WORDS

"For sure needs a liner" is the cheapest possible pool outcome, and liners rarely fail alone. Questions I'd want answered: has the pool been holding water, and if not, for how long has it been down. Does the equipment actually run, meaning pump, filter and heater each energized and observed running, not just present. Is there movement in the deck or coping, because a shifting deck and a torn liner are frequently the same event. And is the plumbing to the pool intact, which is a separate test from the liner and a much more expensive answer.

A pool that has sat empty or low is a different animal than one with a torn liner. Empty pools can float, crack, and have plumbing dry out and fail on startup. Get a pool company out, not the general inspector, and pay them.

The part nobody has mentioned: a pool is a permanent operating cost and an insurance item, and on a two year exit it narrows your buyer pool in most markets rather than widening it. That's a resale variable, not just a repair.

THE HVAC QUOTE MAY BE HALF A NUMBER

A 4 bed, 3.5 bath house often has two systems or two zones. Confirm in writing whether that $8,800 covers the whole house or one unit, and whether it includes any ductwork. Equipment-only pricing on undersized or leaking duct is a number that grows once somebody is on site, and a new condenser on bad duct underperforms, which your buyer's inspector will find in two years.

YOU'RE GETTING QUOTES BEFORE THE INSPECTION, WHICH IS BACKWARDS

Inspection first, then take the report to specialists for the three or four items carrying real money, then total it. Right now you have a firm number on one system and a guess on everything else, which is the exact shape of a budget that doubles. Doing it in the other order costs a few hundred dollars and a week and it's the best money in this transaction.

THE 85 TO 125K OF EQUITY IS WHAT I'D INTERROGATE HARDEST

Where did that range come from? If it came from the agent who wrote your offer, it isn't an appraisal, it's a sales aid. I'd want three actual sold comps with square footage, condition and dates before treating it as real. On a two year live-in flip that number is the entire thesis, so it deserves more scrutiny than the HVAC quote does.

THE ONE NOBODY HAS NAMED

You're planning to live in it while renovating. With $150 a month of margin, the thing that breaks you isn't a big repair bill, it's a repair that makes the house temporarily uninhabitable. HVAC replacement in the wrong season, a plumbing failure, floors going in. If any of that forces you into a hotel for two weeks, you're carrying two places to live out of $150 a month of slack. Price that scenario now rather than discovering it, and earmark a reserve specifically for it.

Last thing, plainly, since you asked for advice instead of encouragement. You haven't signed anything but an accepted offer. The ability to walk away is free right now and it is the most valuable thing you own in this deal. It stops being free when your inspection period closes. So use that window hard, get real numbers on the pool, the full HVAC scope and whatever the inspection turns up, then put the total next to your actual cash. If it holds, you go in with confidence instead of hope. If it doesn't, you spent a few hundred dollars to avoid a two year problem, which is the cheapest outcome available to you today.

Good luck with it. Being nervous rather than certain is a better sign than you probably think.