Q1. >>>if i drink two 500ml bottles of beer at 4.5%abv then that is the same as drinking one bottle of beer at 9.0%
A1. Yes
Q2. >>>if i drink a bottle of vermouth which is 14.7% mixed with lemonade in a mix of half vermouth and half lemonade does this weaken the vermouth to an abv of around 7.5%
A2: Being pedantic, it should be 'around 7.4%' but, broadly, 'yes'.
The easiest way to calculate 'alcohol intake' is in 'units'. 1 litre (i.e. two 500 ml bottles) of 4.5% booze is 4.5 units. 1 litre of 9.0% booze is 9 units.
The current recommended safe limit for drinking is 21 units per week for men, and 14 units for women. The maximum daily ('advisory') limit for men is 4 units. For women it's 3 units.
One or two units of alcohol will impair your ability to drive but almost certainly not put you 'over the limit'. Three units puts most people 'close to the limit', with some people being 'over the limit'. The vast majority of people will fail a breathalyser test after 4 units.
To calculate when your body is clear of alcohol (and you're then safe to drive), allow AT LEAST one hour per unit of alcohol, starting from one hour after you consumed your last drink.
Chris