These questions about modern, new crypto currencies as Doge, Shiba, etc.
Do they normally have dedicated eco system being peer-to-peer payment system, have their server pools, like Bitcoin network? Or these "coins" are some kind abstractions, "tokens" which just can be traded on crypto exchanges?
How do the new cryptos which work like bitcoin with their network and proof-of-work, protect from an attack of someone who has significantly higher CPU power (pool of servers), who can re-do the proof-of-work rebuilding the block chain in the attacker favor?
Do the first coins appear from mining first blocks, or there are first transactions with some kind of initial deposits?
Most of the new coin is not PoW(Proof of Work) but rather PoS and other protocol that they invented. I think you are referring now as modern coin are blockchains token coin, Most the blockchain was coded on a smart contract which means no one allows to edit unless you are the owner of that address.
Most of tokens right now was built on existing blockchain unlike before that it works as Peer to peer on there own separate network.