How to configure eslint indent for WebStorm?

Switch-Case seems to be a special case for eslint regarding indentation. Per default the case clauses are not indented relative to the switch:

"SwitchCase" (default: 0) enforces indentation level for case clauses in switch statements

See here for an example: http://eslint.org/docs/rules/indent#switchcase

You need to set SwitchCase option to 1 like so:

"indent": [
    "error", 
    4, 
    {"SwitchCase": 1}
]

So your complete eslint config will now look like this:

{
    "env": {
        "es6": true,
        "node": true,
        "jasmine": true
    },
    "extends": "eslint:recommended",
    "parserOptions": {
    },
    "rules": {
        "no-else-return": "error",
        "no-multi-spaces": "error",
        "no-whitespace-before-property": "error",
        "camelcase": "error",
        "new-cap": "error",
        "no-console": "error",
        "comma-dangle": "error",
        "no-var": "error",
        "indent": ["error", 4, {"SwitchCase": 1}],
        "quotes": [
            "error",
            "single"
        ],
        "semi": [
            "error",
            "always"
        ]
    }
}

Regarding your 2nd example I think it is common to write it like this:

obj.format('text', {
    value: '${two}'
});

Both parenthesis are opened on the same line, so you close them on the same line. If you use auto format on that lines, they will not change.

The third example looks a bit tricky. I don't know if you can get eslint and auto format on the same page for that one. I personally would prefer the eslint way, but I don't know if you can tweak the auto format to do it like that.

Edit: You could write it like that:

return begin()
    .then(() => callback()
        .then(data => {
            success = true;
            return commit();
        }, reason => {
            return rollback();
        }),
        function(reason) {
            update(false, false, reason);
            return $p.reject(reason);
        });