In the whitepaper v2, I saw a section for inter-blockchain communication. Does this mean communicating with blockchains based on other technologies like Ethereum? If not does that mean that each DApp is its own blockchain? Does every new blockchain accept the EOS tokens for Compute, Storage and bandwidth resources or does each chain have its own tokens, block producers, etc...
EOS is a specific blockchain implemented using the open source EOSIO software built originally by Block One. EOSIO can be used to create new blockchains with varying degree of changes in many areas -- technical and non-technical.
For example, TELOS is such a blockchain based on EOSIO with significant governance tweaks. Similarly, there are other blockchains based on EOSIO software. They are often called the sister chains.
All sister chains are independent blockchains running the core EOSIO software with different versions. Think of this as the Linux distributions -- Red Hat, SuSe, Slackware, etc.
Each sister chain can have it's token and can have tokens that are not available to other sister chains.
Since sister chains are independent, they have their own sets of block producers and thus different main nets.
A dApp can run on many sister chains as the code (aka smart contract) is necessarily the same except for the "native" token. What I mean by "native" token is that the EOS main net uses "EOS" token and all the dApp tokens are paired with "EOS" token in general. So for example, a very popular EOS dApp called DICE has its token called "DICE," which is paired with "EOS" and many other tokens in the EOS ecosystem. The same dApp can be run on the TELOS sister chain and be paired with their "native" token called "TELOS."
A dApp does not need to run its blockchain unless it has some significant resource demands or other business-cases that call for a dedicated blockchain. Such a blockchain -- run by a dApp -- will be called a "sidechain," and it will interact with the primary blockchain via the interblockchain communication (IBC) protocol.
Hope this helps you a bit.