Is there a way to distinguish or calculate the total amount of ether which any account has received from mining and from the transfers (I mean the amount of ether transferred from other accounts)?
In principal all necessary data are on the blockchain. However - to practically get them you will need the help of a blockchain explorer.
Etherchain for example shows the mined blocks for each account. So this is an easy way to figure out how much of the Ether on this account was mined.
@mKoeppelmann suggests, etherchain will have the data. Here is a link to their API documentation - etherchain.org - API Documentation.
You can also use EtherScan.io's APIs.
For this, you will have to register and get a APIKeyToken, but the APIs of interest for you are:
Get Ether Balance for a single Account
Get a list of Account Transactions
Get list of Blocks Mined by a Specific Account - MINED Blocks
Get list of Blocks Mined by a Specific Account - UNCLE Blocks
Technically speaking tokens can be "minted" not mined. Mining is the process to create anew block in the chain with a reward in ether which are "mined" with the block. But tokens are just created as data in a smart contract not really mined.
At least for token based on MintableToken.sol by Open Zeppelin you can easily see that a fresh minted token comes from a 0x000.. address. Here an example of some token minted and sent to users: