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I tried to push it down by hand, nope
This, to me, indicates that the filament isn't loaded into the extruder properly. I've had the same thing happen a couple of times when changing reels. (I've a Geeetech Acrylic Prusa i3 Pro B ) The end of the filament comes off the reel curved so when you poke it through the feed hole it doesn't feed into the top of the extruder tube properly. Try straightening it out before manually feeding it.
Can you "load" the extruder cleaning pin through the extruder? You notice that you'll have to play with the pinch roller to get it in a position where everything lines up. You need to do the same with the filament. Anyway, hope that helps.
Not sure about the other problem. Do you mean that when the print starts the Z axis lifts off the bed by 5 - 8mm? Is the distance the same for different prints or is it arbitrary? Can the same print start at different heights? Can you be a bit more specific? What have you tried so far?
What's the first layer setting in your slicer set to?
Play Bonny!
Soadyheid.