Disclosure: I have not been brewing long and have not added fruit to one of my beers yet.
Green Banana vs Ripe Banana -
I'm not a huge fan of ripe banana and would fear its flavor overpowering the beer and strawberries. I find most strawberry banana products to be more banana than strawberry. I would use a green banana to get a slightly tarter flavor that wouldn't be overpower everything else. If I were to use a ripe banana, I would probably use half the volume I mentioned in the recipe, taste it after a week, and add more if I thought it wasn't enough. The amounts of fruit I stated are speculative based on recipes for other fruit hefe recipes I have read and contemplated for future creations of my own.
The reason to use a puree is to increase surface area. However, that is more likely to make a smudgey paste on the bottom that you will want to filter out. You could bottle it, but it would probably not be visually appealing. You could just chop the fruit up, except it will not absorb as much or fast - although, that is what I do when I make liqueurs - puree is a real pain to filter out. With fruit, the longer it sits in the secondary, the more flavor you will get. At first you will displace the water and get the free sugar flavors. If you freeze your fruit beforehand, it will rupture the cell walls, which will free up more sugar and water and result in faster displacement. Otherwise, you will have to wait, and if the alcohol and sugar ratios aren't high enough a lot of the flavors will stay within the fruit itself.
You can often buy sterile puree of berries, not sure about bananas. I have read of people who haven't sterilized, just clean the fruit, blend it up throw it in, and haven't had problems. However, there are two ways that I sterilize fruit when canning - both of which would work here and are described below.
First, just like a sauce, in a pan, on the stove. This will caramelize some of the sugars and change the flavor profile of your fruit. This is not a bad thing, but it will be a different flavor from the fresh fruit. If you want to go this route, I would taste test a small amount fresh and a small amount on the stove and see which I like most. I cannot remember the exact temperature, but I believe you want to get it to 150F to kill most of the bad bacteria - a google search should be able to confirm this. I know for some things it is up to 180F...
The second method can be done in either of two ways - with plain water or with sugar water. If I was canning it, I would use sugar water. For beer, I would probably use plain water, unless you want to restart fermentation by adding more easy fermentables (up to you, but it will increase alcohol and wateriness of your beer). This method is to sterilize your blender in preparation to make your puree. Sterilize all of the utensils that will come in contact with the fruit. Start a pot of sweet water (the water you would use in your brew - sweet water just means drinkable/clean water). Also, have a pre-boiled (to sterilize), but now chilled pot of sweet water. Then, cut your fruit up, not too small, but not so big that any chambers are open. Also, remove any bad spots. Drop some of your fruit into the hot water to blanch (sterilize) it, leave it for no more than 30 seconds (I would go with 10 seconds, that should be enough), pull it out with a slotted spoon (leave water behind), and drop it into the cold water to chill. Do this for all of your fruit. Then, strain off the cold water, put the fruit in the blender and puree. Toss the puree into your secondary, stir well (don't aerate).
Note - the boil water will have some of the sugars in it. You could add it, if there isn't much, to your beer - but it will lower your SG. Alternatively, you could chill it and drink it if it tastes good. Or just toss it.
Oh, for canning, I do either of those methods above, put into a hot jar the puree or chunks (pretty!) (with or without syrup), toss on a hot boiled lid, put a ring on it, seal it, keeps for quite a while and delicious in the winter months. Then again, with fruit available year around these days, not quite the same thing. Yes, these are a form of fruit preserves.
Hope that was helpful? Let me know if you have any questions.
M
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