Trump knows how to get deals done in the business world behind closed doors. That's very different to making political deals in Washington and lobbying for public support to persuade Congressmen. I suspect his brash public demeanor and extreme rhetoric would make it harder, not easier, to forge bipartisan agreement. Trump will do anything for the attention.
Clinton's unfavourability ratings are significantly higher than Cruz. Cruz might be the second most hated man among Democrats right now, but certainly not nation-wide.
You can blame Cruz for being the one responsible for the shutdown or you can blame it on a government that refuses to scale back spending despite constantly increasing deficits. It depends on your preferred policy views. The Mexico border issue is one pretty much every Republican has to endorse in some way to get through the primaries, but it never comes to anything after elections. The social legislation that's really at stake is DOMA, and Cruz would be against that.
As for getting elected, it's hard to tell. I think he'd have a shot against both Clinton and Sanders for different reasons. Clinton because of her unfavorables and being the establishment candidate (with corruption concerns), and Sanders because he is more leftist. I'm no expert at calling elections though, I'm simply talking about who I'd like to see become President.