Once distillation is complete the resulting alcohol will last indefinitely if stored out of direct sunlight and in cool conditions.
Essences - Technically speaking, essences will never go 'off' as such - there is no risk of microbial spoilage (due to the high level of alcohol), but it will never oxidise ('turn to vinegar' like beer, cider or wine). The taste quality will diminish to some degree over time, especially if there is a lot of headspace in the bottle.
Our advice would be to drink within 2 years so ensure it is at its best. After 2 years, the flavour intensity will begin to fade and the flavour profile will begin to lose some degree of nuance/complexity.
Made up cream liqueurs can keep for 6 months if refrigerated, or 1 month at room temperature. If you decide to use fresh cream as an alternative to the base, then it will only last 5 days in the fridge.