Yes, creating a transaction on an order would update the orders updated_at timestamp. You can see the relationship between Orders and Transaction here.
An orders Transactions array can be written to more than once, yes - but they can only be POST'd to. An order can have no more than 100 Transactions associated to it (docs). I'd heartily recommend having a dive into our Transaction docs both (GraphQL Admin API & REST) which would provide more details. Hope that helps!