It is a clump, not a tree
The single most useful thing to understand about a banana is that what looks like a trunk is a stack of leaf bases, it fruits exactly once, and then it dies. That is not a problem and it is not a disease. The plant continues as the pups around its base.
So the plant you buy is really a colony, and your job is to manage how many members it has. One tall stem plus one or two pups coming along behind is the right shape: the tall one fruits, the next one is already half grown when it does, and you cut the spent stem out at the ground. Left alone, a clump turns into fifteen thin stems that shade each other and none of them fruits well. Cut surplus pups off at ground level with a sharp spade.
Feed it more than you think
Bananas are the heaviest feeders we sell. A banana growing ten feet in a season is building all of that from what you give it, and a hungry banana is immediately obvious: pale, small-leaved and slow. Through the warm half of the year, feed monthly with a balanced fertiliser, and be generous with compost or aged manure around the base. Potassium matters particularly, so a fertiliser carrying a decent K number is worth looking for.
Water goes with it. A banana has enormous leaves and loses water fast; it should never dry out in warm weather.
Blue Java, and what cold does
Blue Java is the variety people come looking for by name, for the custard texture and the vanilla flavour, and for the dusty blue cast on the unripe fruit. It is also one of the tougher bananas in cold and wind, which is why we grow it here rather than the supermarket Cavendish.
A freeze burns every leaf brown and looks fatal. It usually is not. The corm underground survives temperatures that destroy the top, and a heavily mulched clump comes back from the base in spring. Do not cut a frozen stem down straight away: if it was close to fruiting it may still carry on, and the dead leaves shelter the growing point underneath.