Adding UK as a new market or making a new website?

[Aboudaboud]

Hello guys.
So my Shopify store is based in Europe and i sell my products all over Europe. 
I am interested in expanding to the UK so i opened a UK company to start selling in the UK.

My question is, shall i make a fully new store with a new domain + shopify shop, or shall i continue selling on the European store and add the UK as a new market. 

If i decided to add the UK as a new market only, I don't understand is that can i create two different inventories for each ? Inventory for UK and inventory for Europe?

Also,  each invoice has to be generated under a different companies. Invoice for UK customers with a UK company details, and an invoice for EU clients with my EU company details. Is this possible?

Finally, my EU store is set on Euro. If i added UK as a new market for my store, can i change the currency for all the products or it has to be in Euro?

Please note that i have some inventory in EUROPE and other inventory in the UK.

Your advice matters, appreciate your response!