OK, first you have to understand, that Solid Edge 2D is parametric software. This means, that you can connect the geometry with constraints (dimensions, geometric), thus changing your geometry quicker.
For example, if you need to change the diameter of the shaft from 20mm to 25mm, you just type the new value for this dimension. And all the other geometry will change accordignly. You can also connect one dimension with another via formulas (tools/variables).
So, according to this, you can not move just one line so that the others will not be affected. If you want to achive this, then you have to delete proper constraints first. But I am sure, that when you will use the parametric in its full power, you will not want to work without the constraints.
Now, back to your problems.
First problem is with lock/unlock the dimension. I really don't know, why you can't turn the dimension back on. Maybe you should turn off not to scale first and then lock the dimension. See my movie, that I have uploaded.
And your second problem.
Well, this really isn't a problem. The drawing is working as it has to. If you will turn on the 'Relationship Handles' command, then you will see, that you have probably some geometric constraints applied to your sketch. All the lines are connected with endpoints. And somelines are probably horizontal or vertical. Then, you also have all the neccessary dimensions. So, when you want to move the sketch, you can not do this in any direction, because the sketch is almost fully constrained. It seems, that the lower horizontal line is not exactly horizontal. It is placed at some angle. And since there is no dimension for this angle, the line can be rotated.
And then about placing additional dimension. You can not lock this dimension, because the sketch will be overconstrained. You have already dimensioned the height of the sketch on the left side. On the right side, you also have one dimension. So, this third dimension that you are placing is actually overcontraining the sketch. Solid Edge knows, that this third dimension can be calculated from 'left dimension-right dimension'. If you want to lock this third dimension, then you have to unlock one of the other two dimensions first.
And about Maintain Relationship command. You don't have to turn this command off. Nothing will happen to the sketch, you have alreay drawn. This command is just helping you in creating a parametric sketch. When you draw a horizontal line, it will apply the horizontal geometric constraint. So when you are changing this line or entire sketch, this line will always be horizontal. Or when you draw one line from the endpoint of another line, it will apply connect relationship. So when you move one line, the connected line will move, too.
I know that I have written quite a lot. But I hope that it is clear enough. If there is something to be explained more thoroughly, just ask.
