There’s a slight confusion here. Nash Link launched as a crypto payment method on L1: this means you can pay from any Bitcoin wallet (and soon eth/neo wallets hopefully). When making a bitcoin transaction - i.e a Bitcoin transfer - it needs to be confirmed in a block; then every subsequent confirmed block reinforces the probability that this block is “healthy”. This is why centralized exchanges require a certain number of confirmations before crediting your deposit amount to your account. In the case of Bitcoin, 1 block is 10+ minutes which means that if Nash Link required 2 confirmations for payment to be accepted, you would have to wait between 10 and 20+ minutes.
Nash Link on L1 does not “cost nothing”: you do have to pay for network fees like you would for any Bitcoin transfer. However, Nash built a technology which allows it to accept payments as soon as the transaction is detected, meaning that you have to wait less than 10 minutes (likely only a few minutes). This technology is based on risk management, because you can never be 100% sure a transaction isn’t rogue but you can greatly reduce the risk by analyzing the network (googled it).
Lastly, Nash Link on L2 (“Nash Channels”) should be - unless I’m mistaken - instant and feeless. The reason is: say you’re paying in Bitcoin: the merchant wants to receive fiat, so in the background, Nash market sells BTC for USDC, then credits the merchant for the equivalent amount of his desired fiat currency. The point is: just like on the exchange, the transaction is instantanneous and without network fee. Do note that even though this is great, it does require the paying customer to have a Nash account with BTC on Nash Channels to pay with. I’m sure Nash has a well thought-out roll-out strategy for this when the time is right.
That’s an interesting question: a few options come to mind.
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if Nash team is able to find a corrolation between gas price spikes and ETH price movements, I guess they could finance part of the ETH/ERC20 deposit/withdrawal fees of Nash users by hedging themselves. For instance, let’s say that Nash finds the following corrolation: Gas prices soar a lot more when ETH price pumps than when it dumps. Then by holding a sufficient amount of ETH, Nash could pay for (part of) the users’ deposit/withdrawal network fees, only when ETH pumps, while keeping a stable amount in terms of fiat value. To make it more interesting for Nash, they could compensate only deposits… 
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another possibility would be to grant Nash users a trading fee reduction of 100% of the deposit network fee beyond $10 in the limit of $10, for a limited time of 48h and for a maximum of once every week. So if this week I make an ETH deposit which should cost $17, then it does cost me $17, but the first $7 are “on the house”, meaning I can trade as much as $7/0.25% = $2800 in taker orders without paying any fee (in the next 48h only). Obviously this solution is costly: Nash would renounce some of its revenues to alleviate the traders’ pain of paying high fees on deposits. It would also cost in development time.
Obviously there are other ways to help users bypass the issue like implementing less costly chains as suggested by @BananaMan and @D_Raky.
This would not be technically feasible since to remain non-custodial Nash relies on MPC, meaning anything must be approved by both Nash and you, so Nash could not deposit your tokens from their wallet on Nash Channels “in your name” because they would require your signature. Also it would nullify Nash’s non-custodial nature, which is kind of a big deal 
