lines, circles etc.
To do that open up the layers drop down, select the three below layer 0 and at top select the minus sign. You will then be given three options and elect the one to move contents to default layer. If yo now go back and double click one of those components( group) to get in edit mode, then select say a line and then look at the entity drop down you will see it is on layer0. You can then go back to the layer drop down and make a new layer, select that group ( don't double click ) you can re-assign that group to that layer but its internal geometry will still be on layer zero where you want it. I would recommend you use components but not necessary. You can recreate the other two layers and gives you the capability of hiding geo while you model and the others not interacting with each other.
BTW when you use the staryline tool make sure you are in the context of the group( double click first). Also to correct some errors ( like you may have a case where two lines do not quite meet at the vertex in maybe easier to use the move tool to grab the end point and move to the other one. However that can distort geometry so I will often delete one of those lines and move the others end point to the terminus connect vertex of the deleted line. The use of the triangle approach is useful soem times but you should not need it much.
Also if you go to windows preference, extensions, utilities and make sure extensions are enabled then on the tools tool bar fly out it will have a create face option under utilities. That sometimes is helpful because it will say why a face was not created. It is not very robust however.
Hope this helps. You will learn some of these moves as you model more. Its a learning experience
SU implemented an auto intersect in I think was 7 so crossing planar lines in the same context will do what you describe. It is normal. If they are in two different components they will not do that.
good Luck