Splitting a model in half

You need to understand how the selection fence works.
Right to Left (a dotted line box) selects everything it touches.
Left to right (a solid line box) selects everything that is entirely within the box.
Ctrl with the selection adds things to the selection and shift either adds or removes them.

So here you see I right to left select the parts I want to intersect, intersect, then right to left select the right side, the using shift deselect the guides and make it a group.
Then right to left select the left side, deselect the guides and make that a group.

There are many different ways to do things, this is just one example.