Thanks for your questions, which we'll answer in brief:
1. The adoption costs depend on your internal development costs in terms of developing the application on top of MultiChain – this is not something that we can assess for you. The operational costs are simply the costs of running and maintaining whatever server/s you choose to run MultiChain on. It does not have any special or unusual requirements beyond the published system requirements, and of course you need enough disk capacity for your chain's long-term growth.
2. Yes, MultiChain can be extensively configured to make it open or permissioned along many axes. See the anyone-can-* blockchain parameters: https://www.multichain.com/developers/blockchain-parameters/
3. MultiChain has been in development since the end of 2014, so almost 3 years. The first alpha release of MultiChain 1.0 was in June 2015.
4. You do not need any approval from us or any other centralized party to use the platform. MultiChain is simply a piece of software that the blockchain members run for themselves.
5. MultiChain runs on any modern 64-bit Linux distribution or 64-bit Windows – see system requirements at the top of this page: https://www.multichain.com/download-install/
6. Please discuss training with us in private correspondence. But in general our recommendation would be to start with the 'Getting Started' guide and see how you get along – MultiChain is designed to be quite intuitive and easy to use: https://www.multichain.com/getting-started/