Check my answer by following this link: http://checkthishouse.com/qa/27/seal-unused-chimney-after-replacing-furnace-water-heaters.
For the water heater flue just use methods described in the link above.
Assuming that the fireplace gas insert will go directly under the damper of the old fireplace you need to make sure that there is a sufficient amount of insulation above the damper to prevent any heat from that new fireplace from migrating into the old chimney stack and causing condensations.
Depending on the design of the chimney and fireplace’s damper you might be able to tightly roll 2’-3’ of blanket insulation, slide it through the damper, and let it expand inside the flue. If there’s enough room, insert another section of insulation flat on top of the damper.
There are also chimney balloons that you can insert into the flue and inflate it so it tightly seals the space. The manufacturer claims they stay inflated for years but I’m not sure if that would work on an exterior / cold chimney. Low temperature might cause the chimney balloon to lose pressure and break that seal. Since its access will be blocked by the insert there isn’t much you’ll be able to do.
To make the damper air tight add a bid of silicone (use RTV type / high temp.) along its edges (you’ll have to clean its surface first) or use aluminum duct tape to create a seal. Also, before installing the gas insert make sure that all the cracks and gaps inside the existing fireplace have been sealed.
You can also have a sheet metal plate precut and secured tightly / sealed along the edges directly beneath the damper (flue insulation still applies to this one).
Since there’s always a chance of condensation buildup and moisture inside the chimney, its top should be protected so the rain water doesn’t get in, but left open to allow any moisture and condensation to evaporate.
Therefore, install rain caps and protective screens (if missing) to stop rain water penetration and keep the birds / rodents away from the flues. Of course, you’d need to perform mortar and flashing repairs as well.
Let me know if there’s anything else. Thanks