Embed for Customer Direct Query vs Import

I am embedding dashboard into a webiste. We were creating a PBI datasest and connecting multiple reports to it via direct query. We are have performance problems and I think most of them would be taken care of if we switched to Import. 

We are using a A1 Sku for the embed. As I understand it, the A skus relate to compute capacity but not the storage size of the data model. Is this true?

Do I have to pay for storage costs seporately? If so, does that mean I would have to buy premium capacity or how does it work?

I tried searching but I found mostly confusing information so any info is greatly appreciated.