1) Diving dry you mean with a dry suit right?
Yes
2) Diving wet instead you mean with a wet suit right?
Yes.
3) What you mean with DS?
DS =
Dry
Suit. WS =
Wet
Suit.
4) With my questions I mean if you are diving and your BCD brakes and you are unable to pump air in it to go up, what's the best thing to do? will you start going down? is it better to ditch your weights and try to go back up?
As I said, it depends. Are you able to swim up without assistance from your BCD? If I can do that, I'd rather not ditch weights at depth, but I might well ditch on the surface. If I can't swim up, it's time to start ditching, preferably in increments if the situation makes that possible (you don't want to shoot quickly to the surface, and that can happen if you ditch a large amount of weight)
5) Why it makes difference where are you doing the dive if it brakes?
Because where I am makes a difference if I can't swim up or keep my depth without much trouble. On a shallow shore dive, I won't be in immediate danger if I hit the bottom and I can - at least theoretically - walk up along the bottom. On a wall dive, I might start descending to dangerous depths.
6) With diving on a wall you mean a wall of rock where you cannot see the bottom?
Yep. You dive along a more or less vertical wall, and it may be rather deep below you. Losing buoyancy in a situation like that is quite different from losing buoyancy over a flat bottom at 10m depth.
7) With diving in your home water you mean the place where you usually dive and you know well?
I mean in the region where I usually dive, with the water temperatures I usually experience.
8) What you mean with "I'd of course make sure to open my airways on my way up, and I might try to flare out to slow the ascent as much as possible" what you mean with airways?
Do like they taught you in the emergency ascent exercise during OW trainnig: Open your mouth, look up, don't hold your breath, make an "aaahhh" sound.
Go somewhat horizontal, spread your arms and legs to provide maximum surface towards your direction of travel. That will slow down your ascent. Slow is good, especially while ascending. Lower risk of barotrauma that way.
You answer my question anyway in certain ways, but still I'm a bit confused about what to do in this kind of situation, I'm an OWD but I did my course 9 years ago, I just recently start my AOWD and I'm studying so I start to have questions or doubts about some matters and I know that on this community there are nice people like you who knows so much about everything and can help me.
Talk to your instructor about this. If I were in your situation, I'd check on the quality of the AOW class you'll take. Is it a minimum time, minimum cost class, or is the instructor willing to use more time and provide some additional/remedial instruction/tutoring (that will probably cost more)? Since you obviously haven't dived much since your OWD and that was nine years ago, would it be better for you to take a refresher course or re-do your OW before going AOW?