1) these are called repair spurs, you use them to put a rot-proof RC end on a wooden post. They are mostly added when an original wooden post has rotted but you can use them from new, if for example you like the appearance of wooden posts and want to avoid them going rotten (it is essential to raise the bottom of the wooden posts away from the ground in this case) If you like concrete you can use full-height RC posts (and if you want to, you can use masonry paint to make them blend in with the fence. This also makes them last longer as it reduces water penetration in the top. Concrete does not rot, but if it is not dense and has big air bubbles it will take water in, which will freeze and break up the surface, eventually reaching the reinforcing steel and making it rust).
I expect your fence is about 6 ft high, so 2ft of concrete spur underground, and 2ft above, bolted to the wooden post, will be right.
2) it is usual to backfill the hole with concrete and rubble, because where you dig it out you will have loosened the soil so the post will move relatively easily. Unless you have an unusually sheltered spot the wind will then rock the post about and it will get looser and looser. It might be possible to ram some kinds of soil down hard enough, but I live by the coast and haven't tried it.
3) Enough to fill up the hole (!) so make the hole as small as you can; try not to have a cone-shape with a big top, as more of the strength comes from lower down. One day you will have to dig out that post, and you will find it very difficult to get out a barrowful of concrete with hand tools. It will also obstruct your flower bed/lawn or whatever. If you are not doing it for a living, and can spend a bit of time on it, you get a neat result if you put a bit of scrap wood shuttering around the post at ground level, and just have a inch or two of concrete showing as "shoulders" round the post at ground level. You can economise on mix by packing in clean bricks or lumps of old concrete rubble, or big stones a "plums" in the mix. No mud or soil on them though.