Hi, I've looked over the API you provided and I'm positive the data can be extracted and imported into a Magento store, no matter if you plan to use Magento 1 or 2.
Relevant Skills and Experience
I've been working with Magento for the past 4 and a half years, and in this period I've had the chance to work on multiple projects that required importing data in one way or another.
Proposed Milestones
kr200 SEK - Create Magento store views based on the API Fronts
kr400 SEK - Import categories
kr3800 SEK - Create extra product attributes with option values and import products with stock, price and images
kr400 SEK - Create extra customer attributes and import customers
Additional Services Offered
kr300 SEK - Hourly price for extra support
Are you using Magento 1 or 2?
What type of products do you sell, do they have special price rules?