What buffer and spring length  should I use for braced .556 lower?
Also do I need to change the buffer detention and spring?
Thanks in advance

The same type buffer and action spring are used for both 'pistol and carbine receiver extensions'. Same buffer retainer and retainer spring also.
Hopefully that helps.

The simplest answer is carbine length. There are several braces that even use a carbine receiver extension (most of the adjustable ones). There are a few PDW braces, CMMG for example, that are shorter and use proprietary buffers and springs (included with brace).
If you're using one of the old school braces that slips over a pistol buffer tube, just go buy a complete buffer tube kit that comes with the spring and buffer.