What is the difference between 'Net ROI (1mo)' and '$ ROI (1mo)'?

$ ROI (1mo) shows your returns measured in USD. This simply looks at $ difference over 1 month period.

Net ROI (1mo) is the impermanent gain or loss you would have experienced if you were providing liquidity for 1 month. In other words this shows whether you were better off pooling or just holding your underlying assets. If negative, that means you would experience impermanent loss supplying liquidity to that pool over 1 month. If positive that means exchange fees generated by that pool, outweighed any losses due to price fluctuations during that month. Best case scenario for liquidity providers is when you ADD and WITHDRAW liquidity when underlying assets are around the same price.

Lets say for example you join ETH/DAI pool with ~3000 when price of eth is $300. Your pooled assets would = 5 ETH + 1500 DAI. Now lets say 1 week later price of eth doubles to $600 (depending on volume) you could have something like 3.7 ETH + 2220 DAI which means your $ ROI is $4440 - $3000 = $1,440 but if you held original assets in your wallet you would have $4500 - 3000 = $1,500 so $60 is that imp loss portion. This increases as your exit price gets farther and farther away from your entry price.

To sum up, your best bet is to come in and come out when prices are relatively the same. Because in this case you will get back relatively the same proportions you entered with + accrued fees from swaps that happened during your pooling period. With eth/dai pair its easy to track this, but keep in mind when you have pairs like eth/snx - the ratio is counted relative to each other. Meaning if during your pooling period both ETH + SNX go up in USD values at the same rate - you will still come out with the same ETH+SNX proportions

Are there any fees besides standard Ethereum network transaction fees for using Zapper?

No, currently Zapper does not charge any fees.