The exact charge has been published by GivEnergy and is £4.99 a month with the first month free. It could of course go up in the future, especially if not many people subscribe. Conversely if too few people subscribe the portal may still go away altogether and the software entity wound up.
We are launching in May for a price of £4.99 per month. This includes VAT and payment processing fees. This price reflects an honest assessment of the platform costs, divided by our expected userbase of GivEnergy Premium, given the survey feedback.
All revenue will go to supporting the software and building new features that will save you more money. We don’t intend to make a profit from this, and we will review pricing in the future if this happens.
For local API I don't believe it is a REST API as you might be used to with the cloud. The easiest way to get data out of it will be to use GivTCP on Home Assistant. As a bonus you can put PredBat alongside it to manage your system for the lowest cost/carbon/some combination thereof.
I am not sure there is public documentation of the API but you could probably design one based on the GivTCP code if you are desperate to build your own.
GivEnergy-local is another Home Assistant project which I believe does similar things and could be another reference for rolling your own.