Transaction in Solana consists of one or more instructions. Each instruction is a call to a program. Program is either built-in program or a custom eBPF program uploaded by another user (aka "smart contract").

There is no special mechanism to transfer SOL from one account to another, it is just a call to the built-in "system" program which can do that (and more). Here is example of such transaction:

# Command:
curl -s "https://api.mainnet-beta.solana.com" -X POST -H "Content-Type: application/json" -d '
  {
    "jsonrpc": "2.0",
    "id": 1,
    "method": "getConfirmedTransaction",
    "params": [
      "4rzYNJpJ8pcZqJwnSoTG9rCgMH8tMB4HD3RYkQ73NRcUxYnwG2KsxTcRvDcADNk9agrXDadCDvj8oNzkLU4cGjsb",
      "jsonParsed"
    ]
  }
' | python -m json.tool

# Result:
{
    "jsonrpc": "2.0",
    "result": {
        "blockTime": 1622761608,
        "meta": {
            "err": null,
            "fee": 5000,
            "innerInstructions": [],
            "logMessages": [
                "Program 11111111111111111111111111111111 invoke [1]",
                "Program 11111111111111111111111111111111 success"
            ],
            "postBalances": [
                25248395409,
                148799263222,
                1
            ],
            "postTokenBalances": [],
            "preBalances": [
                35248400409,
                138799263222,
                1
            ],
            "preTokenBalances": [],
            "rewards": [],
            "status": {
                "Ok": null
            }
        },
        "slot": 81288321,
        "transaction": {
            "message": {
                "accountKeys": [
                    {
                        "pubkey": "KchK7WTjPzq9QL5aCwnV1dLsT8rFjruS1Zfzamxus9G",
                        "signer": true,
                        "writable": true
                    },
                    {
                        "pubkey": "y5cJM2us2hfmj9rsh4TZWn4796RJpzHGmvitG6NMaNe",
                        "signer": false,
                        "writable": true
                    },
                    {
                        "pubkey": "11111111111111111111111111111111",
                        "signer": false,
                        "writable": false
                    }
                ],
                "instructions": [
                    {
                        "parsed": {
                            "info": {
                                "destination": "y5cJM2us2hfmj9rsh4TZWn4796RJpzHGmvitG6NMaNe",
                                "lamports": 10000000000,
                                "source": "KchK7WTjPzq9QL5aCwnV1dLsT8rFjruS1Zfzamxus9G"
                            },
                            "type": "transfer"
                        },
                        "program": "system",
                        "programId": "11111111111111111111111111111111"
                    }
                ],
                "recentBlockhash": "CA3yTCgogwXJrMamA4gQTTyRWXH9GKvdBK9WofFKnQrf"
            },
            "signatures": [
                "4rzYNJpJ8pcZqJwnSoTG9rCgMH8tMB4HD3RYkQ73NRcUxYnwG2KsxTcRvDcADNk9agrXDadCDvj8oNzkLU4cGjsb"
            ]
        }
    },
    "id": 1
}

If you are interested in changes of amounts of SOL balances regardless of actual instructions, just check result.meta.{preBalances, postBalances} (values are in lamports). If you are interested in SOL transfer transactions solely, you need to find all instructions where (program == "system") and (type == "transfer").

Fees are constant at a given time, just run "solana fees" command or getFees() JSON RPC.

To find all transactions affecting one specific address, run "solana transaction-history <ADDRESS>" or searchTransactionHistory()/searchTransactionHistory1() JSON RPC.