Yes, It will be 4 different attachments as you mentioned. Yes, the cross-AZ traffic would be free of charge as mentioned in the link above. For pricing, you will be charged, AWS Transit Gateway hourly charge & Transit Gateway data processing charge.
Refer to https://aws.amazon.com/transit-gateway/pricing/ to be exactly sure of the pricing.
Hope this answers your question. for any detailed queries regarding Pricing, please contact AWS Support.
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