To me solo mining is still a mistery untill now i had 3 times a block but it never got rewarded and there is hardly any explaining about how and what is happening when mining with cgminer and such
If you didn't get a reward you didn't get the block. That simple. You can check the block explorer and see who got the block (if you know the last block completed when you were minning).
Does it really stop finding the correct block when you stop a miner or does it continue where it left off
There is no such thing as "left off". Each hash a COMPLETELY NEW TRY. It is like a lottery ticket. If you buy 100 lottery tickets and lose and then take a break (turn if off) when you come back and buy a new lottery ticket are you "closer to winning"? No. Each lottery ticket has exactly the same chance of winning.
At current difficulty if you perform 1 hash your chance of "winning" the block is exactly 1 in 7,255,634,282,020,860. It doesn't matter how many hashes you have done in the past your next hash has exactly a 1 in 7,255,634,282,020,860 chance of winning. If it wins you sign the block. If it doesn't win it is COMPLETELY WORTHLESS and your next chance is no higher than 1 in 7,255,634,282,020,860. Your computer keeps playing this lottery until you find a block or give up. If your card is 100MH/s you are making 100 million lottery attempts per seconds.
If so why does the solo server gets new blocks assigned to it ?
If anyone on the network finds a block (which happens roughly once per 10 minutes) then you can no longer try to solve the current (which is now old block) and instead must solve the new block.
And yes the client never reports anything other then if it found some kinda valid block, but again i never got any reward for it.
Something else i noticed is that the block count on the local bitcoin server i run changed a after it found the so called block, but again there is so little support on this local mining that its almost sad.
If the block counter increases it means SOMEONE has found a block not that you have found a block. If you have no generated transaction then you didn't solve the block.
I have found till today no explaining about nor has there been any improvement to see on this what your doing
Thats why i switched to mining in a pool, cause this whole local mining is full of misteries and lack of info
I wonder if anyone really know what it is really doing or where that hidden guy is
Solo mining isn't hard however it sounds like pool mining is better for you. Honestly given there are pools with 0% fees (some with negative 5% fees) I have no idea why anyone wants to solo mine. I have 10GH and wouldn't solo mine with less than double that. Even then I wouldn't solo mine without a reason (I might if there were no non-hoppable pools w/ fee less than 3%.
Honestly I just don't see that this appeal is with solo-mining. In the long run your reward is exactly the same (minus any fees) and in the short run you can have some awesomely bad luck and go months or even years without finding a block.