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Structural in that they hold the ceiling up - though should be redundancy (touch wood!) - but not holding the roof together (generally..!)
Before i cut through one of them temporarily braced across them with a 2x4 from above to be sure.There's usually a decent bit of play in the 'lip' of the hatch that you screw into the timbers, so you can afford to be a within a few mm or so.
Hopefully the existing ones are parallel - I just used a set square when adding in the bracing between them top and bottom.
Yes