Just curious..
As a Petrus user I think I'm solving a "half-cross" before finishing the first block (corner/edge). Or am I missing something..?
Yes you can think of it this way, but I wouldn't recommend to solve this way a lot. I am a Fridrich solver but I'm a bit more free form with the cross in that I also sometimes start with a 2x2x2 and build off of that. Whenever I start with a 2x2x2 it's very rare that I solve 2 cross edges and then a corner edge pair. For 2x2x2 I recommend to try to follow 1x1x2 -> 2x2x1 -> 2x2x2 most of the time. This tends to save moves.
As to the OP about solving cross, try to plan out a blindfolded cross execution of 2 pieces. So inspect and plan all the moves necessary to solve 2 cross pieces. Then close your eyes and solve those two. After that re-inspect to try to figure out the moves for the other two and repeat. Work up to doing 3 of the cross pieces, then all 4.
Also don't be afraid to start with a 2x2x2 on occasion. This, for a Fridrich solver, is the cross with a corner edge pair already placed. It makes it a bit harder to insert the other 2 cross pieces sometimes, but usually it is not too bad. Experiment with Petrus also, see if you like more a block building approach for the start than just always cross. Remember that the goal is to solve the cube, but it does not matter how you get there. So pick a way you like.
Chris