I don't have enough exposure to all the cards to see a way to accomplish what I want, so I'd like some help in trying:

1. Initiating a power challenge in the marshalling phase, is it possible?

2. Putting a non ambush character into play from hand without a specific ability on that card which allows it.

Any ideas?

1- I don't think so currently.

2- The Battle of the Blackwater, Desperate Tactics, Gates of Winterfell, all the Reinforcement events, Jon Arryn, Aeron Damphair, Varamyr Sixskins, Fallen and Reborn, Bound by Blood... the list goes all. All of those cards have either deckbuilding or play restrictions, though. I don't know of a card that can put any character into play, whenever you like.

I guess my diabolical plan to try and get Raiding Fleet out in a 4 player melee in the same phase where a Kraken Tattoo'd Raider could hit for a power challenge after being pumped 24 times and then using We Take Westeros! to make someone drop nearly half their deck on one shot into the discard pile is shot then. I guess I'll have to settle for the appreciable synergy between new Euron, Kraken Tattoo and going last in challenges. If only the tattoo weren't so fragile...

Raiding fleet is only when you "play" so "putting into play" in the challenges phase with desperate tactics or what not wont trigger it...

Your best bet is for a challenge during the marshalling phase... which doesnt exist yet for power challenges...

only intrigue with "Shadow Politics", and even then its fiddly cause you also have to somehow get gold before the marshalling phase... or play hidden chambers...

You can get a military challenge in the Marshaling phase by killing Lucas Blackwood. So yeah, intrigue and military outside of the challenge (or epic) phase is possible, but not power. Yet.