Are you familiar with the Highway Code, as you don't drive? I don't know how much of it's covered in Cyclecraft, but it might be worth getting hold of one of those Theory Test CDs aimed at learner drivers or motorcyclists - they include random multiple-choice tests, might make it a bit more interesting than just reading the Code. I know they're aimed at motorised road users, but it does no harm to see things from their point of view sometimes.
If you're travelling slowly I suspect you'll have fewer issues than those of us who've been cycling for longer and go faster - many drivers seem to be calibrated to expect cyclists to go at no more than 10mph.
Don't be timid around parked cars, but DO pull out gradually and avoid being too close to their doors. Before pulling out try to look behind you, just the head movement can be enough to make a car driver realise you're looking to move out. You shouldn't need to signal every time you pass a car, unless you find yourself being pushed out of the traffic flow.
There's absolutely no shame in walking across difficult junctions, particularly right turns - and you'll soon get to know which junctions are tricky, which ones are OK, and which routes are best. When you start out it's natural to follow the main roads or bus routes if that's what you know, but it's worth exploring the alternatives.
Don't feel you have to filter up the side of traffic at the lights - unless you're sure you can get to the front you're best staying in the queue - position yourself in the centre of the lane to stop vehicles stopping alongside you which may then turn left having forgotten you're there.
And most importantly - keep well clear of lorries in queueing traffic - they have huge blind spots and probably won't know you're there.
Take care out there and you'll be fine.