Chimney venting questions

One of the chimneys in our 100+ year old house is used to vent a gas hot water heater, which leads to a couple of questions...
1. The chimney has a metal liner in place but it begins maybe about 12 inches above where the water heater vent joins the chimney. This leaves about 2 ft of unlined chimney (including about 12 inches below the vent pipe where there is a cleanout access). Is this ok?
2. On one side of the chimney there is a 10 inch round sheet metal cap sealed around the edges with furnace cement that closes off what looks like an old furnace vent. Our home inspector mentioned that this should really be more "permanently" closed off with cement. - Is that really necessary or is a sheet metal cover good enough? - If it should be cemented (or bricked) off, is that a simple DIY project and if so, what do I need to do to make it work?
3. If this chimney is only being used to vent a gas water heater, how often, if ever, do I need to get the chimney cleaned out? (and how do I know when it needs cleaning?)
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