So far as taste is concerned, they do not taste anything like cherries and the flavor is highly variable depending of variety, stage of ripeness and growing conditions. They have to be harvested when fully ripe, which with the most common varieties is a very deep deep red, not orange or pale red but deep red. If not eaten fresh and ripe you might find yourself inclined to spit them out. If you've ever tried a Persimmon they are similar in this respect, both taste obnoxious unless they are fully ripe. If devoured at the peak of perfection they are absolutely fantastic and you'll find yourself feaning for more.
In the warmer areas of deep southern states it is considered an invasive plant as they grow wild in some parts of Florida and Mississippi after being introduced to North America in the 1930s. They will only grow in very warm areas and will die off fairly quickly in temperatures below 30 F. So far as growing them indoors in cooler regions, sure it's feasible as they are not all that large and cumbersome only averaging about 5 feet high at most, let me know how you make out should you decide to try it.
The Surinam Cherry tree is actually a small shrub reaching only 5 - 6 feet at most, and will tolerate most soil types. It will not tolerate salt marshy areas, cold or full shade.
Full Sun - Warm climates averaging at least in the 70s preferably a tad higher.
Water - modestly till established, although it will withstand standing water this is not advisable.
Standard fruit tree fertilization. High phosphorous for fruit production.
No known pests , which is one reason it is considered an invasive plant in some regions.
Surinam Cherry trees will spread out quite a lot and pruning is sometimes needed. A light pruning can actually stimulate fruit production, just don't get carried away.
Cut the youngest and smallest branches back to the first lateral junction. Older branches that are damaged should be cut to the trunk. They can be pruned into a hedge like structure for aesthetic purposes, but this is only advisable if you are a seasoned gardener familiar with pruning practices of this nature. Heavy pruning can destroy the plant or its ability to produce fruit.
Unusual Fruits and Berries Plums Kajari Melon Jujube Fruit
Peaches Snotty Gobbles Miracle Berry Jostaberry