When you say coffee plant I assume you mean the tropical evergreen from which we get the coffee bean.
Coffee plants will grow in a pot rather easily, they will require constant moisture, but also require fast draining potting soil. Mind these come from the tropics where there is heavy and plentiful rain. Coffee "tree" shrub grows best on hillsides in their native environments.
You don't actually need to fertilize coffees, however if you do then they should be fed every 2 weeks from March to October, and then monthly from November through February. Use a soluble, all purpose (10-10-10)fertilizer. This will maximize the production. I prefer a "compost tea" which basically is soaking a shovelful of compost in a 5 gallon bucket of water over night, either dipping the brown water out of the bucket, or pouring through a screen into another bucket.
Coffee beans will not be produced until the 6th year.
Natural or "wild" coffee trees will grow between 16 and 40 feet - in coffee plantations they are pruned and kept at 6 feet for ease of picking the bean. Coffees can be kept smaller than that, can be pruned way back once in a while.
Best growing temperatures is between 65 to 75 degrees F.
Watering:
The finger method is the best approach. Around here there is Watering Day for the indoor plants. Some of my plants require weekly watering, some require two weeks. a few require more than once a week watering. In winter I tend to need to water more since the furnace tends to dry out the air (reduce humidity).
The type of pot you are using will have a huge impact on how often you water. Terra Cotta (clay) pots unglazed will dry out much faster than plastic, and somewhat faster than glazed "finished" pots. If you like the look of plain terra cotta then I strongly suggest painting the interior of the pot with a good exterior paint - a couple three coats will seal it and prevent the salts from leeching through (usually causing a whitish buildup on the outside) and will reduce the need for water.
Water from the tray/Drain pan only with the exception of watering with a compost tea or a liquid water mixed fertilizer. This means you need a flat bottomed tray, not one that prevents the pot from sitting in the water. Most times your tray/drain pan will be the right size for the pot. Fill that half full of water and let the water wick up into the soil. Half full will usually be enough water. Watering from the top will leech out the nutrients from the soil (thus the water in the pan turns brownish) leads to under watering of the roots and throws off the finger test for moisture.
You should be able to insert your finger to the first knuckle in a potted plant - if you can't (Due to the roots) its time to re-pot to a larger pot. That depth is is the best depth to get a good idea if the plant has enough water.
Any new pots or plants I get I check the moisture every other day until I get a fair idea of how long it takes for the plant to drink up the water out of the soil. I also watch to see how much water the plant takes up in about an hour after filling the tray. If water is left after an hour I empty the tray and use less water the next time I water. After that I have my established watering days which I keep religiously.
I tried a variety of moisture sensors and find that they usually end up being wrong which results in under or over watering. I think that they are actually reading the humidity in the air which around here is fairly dry all the time.
White fuzz on your bean is mold - not good. It means too much moisture. I think (not to certain on the coffee) that soaking 24 hours in water will help germination. Most often folk roll beans/seeds in a hormone of B mixtures which help germination and provide an added early growth boost to the seedling. It is sold as a growth hormone.
If your fish water is fresh water (non-salt) then it is ok to use that for plants. If you have salt water fish then the water will kill your plant in time. Plants (most) do not like salt water (except of course those that grow in salty conditions).
As an aside:
Some of my indoor plants go out side in the summer. Coffee trees like that too. Once a month I take my potted plants and put them in the shower, I run a cool shower for about 5 minutes spraying the leaves with a spray (they do not like the massaging shower head
) this not only washes off the dust, but it adds moisture to the leaves. I let them "drip dry". Around here that takes place after the dog's bath. Ferns and a few of my tropical rain forest plants I spray with a misting spray bottle (similar to say window cleaner spray bottle) to keep the humidity around the leaves higher. I use distilled water for that since we have well water which has a lot of minerals that will lead quickly to a white build up of mineral deposits on the leaves.
I also mulch the pots around here. Last time I used shredded bark, but I have used coffee beans, cocoa bean husks and other mulches not only does it finish off the plant making it look like an professional potted plant, it also helps to hold moisture in the soil reducing the amount of water the plant needs. Coffee and Cocoa (chocolate) also have a wonderful scent to them.
