As with everything else Brexit related, technically the UK won’t be bound but practically it will have to choose between following one of the three major economic blocks — EU, USA, China — or struggling economically because they refuse to believe the Commonwealth is not on that list.
Yep, I think the current understanding is that all EU laws will still apply - they kind of grandfather them in - with the understanding that they could repeal them at a later date (as they can for any law).
AIUI, the GDPR by itself doesn't apply to the UK (or any other EU member state in particular). Instead, the GDPR forces member states to enact laws that implement those rules.
This means that, after Brexit, the GDPR implementation laws will still be law in the UK. Depending on the outcome of the Brexit negotiations, the UK might or might not be in a position to repeal those laws at their own discretion.
the key word is General Data Protection Regulation. Regulations are law, and apply directly, no local implementation needed (except for "interfaces", e.g. in the case of GDPR changes to existing laws to clarify how they interact with GDPR and to make exceptions GDPR explicitly allows the states to make)
Directives are the ones that only direct the states to enact laws implementing them.