Can I overtake over chevrons?
The letter of the law: You may overtake over chevrons if the line around the chevroned area is a broken one. Only in an emergency can you legally enter a chevroned area surrounded by solid white lines.
The reality: Solid lines can be mistaken for a broken one because of cat's-eyes, but generally, solid lines border chevrons next to slip roads and potentially dangerous junctions, while broken lines are used around the areas in the middle of the road, used by traffic waiting to turn off. Be certain, though - the police take a very dim view of the crossing of any kind of solid line and, if an incident does occur, the law will be firmly against you.
Can I pass stationary traffic in the face of oncoming vehicles?
The letter of the law: Such a manoeuvre is technically overtaking, and is therefore legal. However the Highway Code asks that, when overtaking, you 'make sure the road is sufficiently clear ahead', which of course it won't be.
The reality: Being narrow, bikes can do this. In many instances, even if vehicles are coming both ways, you can easily fit between the two lanes. Again, it's all about your conduct. If space becomes tight then you have to ask yourself if what you're doing is 'careless'. If you have to cross the centre markings, and, to an extent, you're relying on the goodwill and attentiveness of oncoming drivers, people might get upset. Also, if your riding is aggressive and forceful, you're more likely to get noticed and lose that sympathy vote.