Is it possible to get the tracking number from ShipStation on multiple orders, when combining and sending to same address?

No, it is not possible to get the tracking number automatically updated on multiple orders when you are combining the orders in ShipStation and shipping it. This is the limitation in current integration from ShipStation’s side. Each line in ShipStation Order has a line key which contains a reference to Pressero order item. If you combine orders this value is lost and that is why these order items do not receive shipping information.
With the current integration, ShipStation will only create a record for one surviving order once the orders are combined. Once that is done, the status change and the tracking number will only update for Pressero order that is associated with this surviving order in ShipStation for other orders you will need to update the information manually, through Admin > Orders > Edit Order > Shipping.