I would like to grow African Violets as houseplants.
Often used are bottom watering pots! This article will explain in greater detail: https://www.gardeningknowhow.com/houseplants/hpgen/bottom-watering-plants.htm
https://www.gardeningknowhow.com/houseplants/african-violet/african-violet-care.htm
Will the plant bloom next year?
It is risky, since they are so sensitive to infection, but they tend to shoot offsets when the top is cut. Just know that if you attempt this without perfect sterility, then there is a great chance that you could lose the plant to infection.
Here is an article that will help you with African Violet care: https://www.gardeningknowhow.com/houseplants/african-violet/african-violet-care.htm
How often should African violets be fertilized? And when? After they start blooming or before?
You can fertilize at every watering. Here's how:
https://www.gardeningknowhow.com/houseplants/african-violet/african-violet-care.htm
I have several that are really clumped in the center.
Two things come to mind. Perhaps you are fertilizing too much, and/or, if you're not using fertilizer specially made for African Violets, you may be feeding the green growth but not encouraging the blooms. I would get some African Violet bloom fertilizer, and clip the leaf clumps from the middle. This should make the plants spread out a bit. If it were just one of the plants doing this, I'd say it needs to be repotted, but since they're both doing it, something isn't quite right. Here's a link for several articles that may help:
I am not sure how to fertilise them
As long as it is labeled for use with African Violets then sure! The proper NPK values will be 14-12-14, so as long as these are the ratios of the food, and it contains ammonium nitrate and NO urea then it will be suitable.
Here is an article that will help:
https://www.gardeningknowhow.com/houseplants/african-violet/fertilizing-african-violets.htm
I took a cutting from an african violet and started it in dirt. The leaf looks very healthy but it has been over 6 months and still there is no new growth. What have I done wrong. Billy St. Rose
They are quite particular about their care. It would seem that the environment around them may not be ideal. This article will give you information on the care that they require:
https://www.gardeningknowhow.com/houseplants/african-violet/african-violet-care.htm
Bottom leaves drooping, getting mushy then coming off. I’ve lost almost all bottom leaves of my best plant. I’m desperate. I don’t eat to lose her.
This is, likely, an overwatering issue, or that water is getting on the leaves. This will cause disease, fairly quickly.
Proper care is paramount when growing these picky flowers. This article will help:
https://www.gardeningknowhow.com/houseplants/african-violet/african-violet-care.htm