From memory I do recall that there may be a filing requirement if you purchase chargeable assets in a given year. You would typically enclose these details on a Form 11 or Form 12 (depending on your taxable status). A Form CGT 1 may also be used. However I would say that this filing requirement is missed in a large amount of cases so I personally wouldn't be too bothered if I missed (and I most certainly would not make a back filing). I would consider it as more of a minor venial sin rather than a mortal one.
Your second question is that you can add broker fees and stamp duty to your base cost.
As far as I know you just need worry only when you dispose of the the shares. On a daily baseis there are probably thousands of transactions with people buying shares. If everytime someone buys shares needs to inform the revenue, they would be inundated with extra bureacucracy. It makes no sense. I lived in different countries in the western world and never came across a place where you need to declare that you bought shares.