The "+" sign shows the origin of the board. In other words, it is the bottom left corner. Trying to place components below or to the left of it will give you the error because you are trying to place it off of the board. I suggest you select all and do a block move to the right, so that you can fit more components off to the left.
Yes, but it's not too small. It's large enough for most basic projects. I prefer to be able to see the border, which I think is a layer you can turn on.
You can't manually change the size of the boards in Eagle Lite. You use what you want, then shrink the border around it. But, since you don't show the border, you need to find which layer it is and turn it on. That way you'll be able to see how much space you have. Did you do a block move up and to the right slightly? That will put your parts closer to the center of the board.
Eagle will not allow you to place parts outside the board. This is how they keep you from making large boards on the free version. If you started with a schematics the parts will all be sitting outside the board waiting for you to place them.
as DerStrom8 already correctly mentioned you're trying to place components outside the allowed board size of 100X80mm (3.9X3.15").
I suggest to draw the maximum board "frame" using layer20 (dimension layer) and a trace width of zero. Draw the "frame" with positive values for the X and Y coordinates starting at the reference cross.
With other words, draw the box to the right and upwards only starting out at zero X and Y.
You can move your components freely within that box.
After having placed all components and routing is finished you might shrink the board for the final size. (Select "move" and grab one line of the dimension lines. If the entire box gets distorted grab the line again and align the box for right angles.
Allow free space of at least one trace width between copper traces and the "frame".
I also suggest not just to draw a PCB design. You should rather draw a schematic and connect components using nets. When done type "board;" and Eagle will create a board with the maximum allowed "frame".
Switch "window" --> "board" to see the result.
Group all elements and move them into the "frame".
You will notice that all components are connected with air wires which you might route either manually or use the autorouter.
Don't use a grid size smaller than 0.025". Smaller grid sizes will lead to countless angle errors when using the autorouter.
You can't manually change the size of the boards in Eagle Lite. You use what you want, then shrink the border around it. But, since you don't show the border, you need to find which layer it is and turn it on. That way you'll be able to see how much space you have. Did you do a block move up and to the right slightly? That will put your parts closer to the center of the board.