No. We aren't paying to leave. We're fulfilling longterm commitments (if we have any sense of honour left).
The EU does its accounts in a very odd way. In that the Commission authorises a lot of speculative spending, which can in rare cases take over a decade to happen, or often not happen at all. They work on the same principal as airlines over-selling seats on fully booked planes, because some people always fail to turn up. So the Commission will authorise more spending committments than it has budget for, as the project can't go ahead unless their funding is matched in-country, and then wait to see what happens. Makes the budget a right old mess. This leads to a lot of under and over spends, which will hopefully net off against each other.
Anyway, the Commission's argument is that we're still on the hook for a bunch of these projects that were authorised while we were members. But we're not due any of the benefits from the things we paid for while members. Which is utterly illogical. Apart from the pensions of EU civil servants and the loan guarantees to Ukraine, I can't think of any other major financial committments we are morally or legally on the hook for (though I'm sure there are a bunch of smaller ones).
The EU has legal personality since the Lisbon
constitution treaty. - so makes all its financial committments in its own name. Therefore if it's a club, we owe the fees while we're a member and not afterwards. Otherwise, if we owe ongoing fees, we also own our share of the assets. And should net our share off against our liabilities.
I think the legal position is very clear. And so, I suspect, do the Commission. Which is why they refused to even start to negotiate anything else, before getting a huge financial committment agreed.
So no, morally I don't think we're on the hook for £35 billion. Or legally either.
I wouldn't have done the negotiations like this. I'd have offered a settlement for EU citizens living in the UK (guaranteed whatever the outcome) and a large payment to cover this stuff at the beginning, and a couple of options/suggestions on the ongoing trade relationship and let the negotiations start from there. But actually it hasn't been the British government that have made the negotiations so adversarial - that's been pretty much all down to the Commission. They've been the ones doing the leaking (and what looks like some outright lies) on a regular basis, while May didn't stoop to that level (perhaps she should have?). It looks like pretty much the same playbook as in the negotiations with Greece. And they were the ones who started deliberatly with talk of a £100bn UK payment in order to be politically unacceptable and poison the atmosphere - when it was obvious to anyone that a payment could have been negotiated in parallel with everything else - on the simple grounds of no payment no goodies. Doing it simultaneously makes it a lot easier to sell, so it was pretty clear they were deliberaly trying to make political difficulties for May's government. Which may well have backfired - and led to a situation where no deal is now quite likely. Though the treaty is clear that the Commision does not have the comptetence to negotiate the exit deal, that is in the competence of the Council of Ministers, so it could just be a bit of good cop bad cop thing.
Oh, and you're wrong. We're not negotiating the aftermath of leaving. We're negotiating the exit. The Commission have refused to do that until the transition period - i.e. once we've actually left.
Article 50 states that the Council of Ministers shall negotiate a withdrawal agreement which takes account of the future relationship with the leaving country. But a future trade deal is entirely within the legal competence of the Commission, and they've refused to even discuss that until we're a third country. i.e. during the transition period. So what we're currently negotiating is all the nitty-gritty of how to leave and all the institutional fall-out from that. With an outline of the future trade/security arrangements to be agreed later. Then, after we've left, we negotiate the detail of that outline understanding - during the transition period. When we'll trade as if we're still in the EU, but not be part of it. Hence the security relationship now going titsup, because that isn't part of the transition agreement, but the Commission has barely even started talking to us about that and has surprised us with its initial uncooperative position. Given our current position is to offer full cooperation at no cost (i.e. a huge benefit to other EU members) and the Commission's current position appears to be to reject some of that free cooperation and demand we pay a cost to offer some of the other things we contribute.
I thought "no deal" was a 5-10% chance back in 2016. It's looking like 30-50% at the moment. But I'm seeing rumours of Barnier losing influence - so I wonder if he's pushed a bit harder than he was supposed to? We shall see. At the moment even a Canada style trade deal is off the table, which I do find a bit surprising.