If I bring back a character with a shadow crest does that character go to the field or to shadows. If it goes to shadows what happens at the end of the phase is it still discarded.

It does say to "put it into play", so you do just that. Shadow cards are only special when marshalled and if an effect is intended to put cards into shadows, it will say so explicitly (On My Oath, City of Lies, Blackwater Bay).

For the second question, if you do get the character into shadows (with Cape Wrath, for example) after you resurrect it with Fiery Kiss, then it isn't in play at the end of the phase. In that case, it escapes the discard effect and remains on the board.