Ruling: T.G.1-EM1

If one activates lets say smashing ground and targets my T.G. Warwolf and i chain TG1-EM1. when we swap monsters does the Warwolf still get destroyed?

Smashing Ground DOESN'T target.

Whatever monster you're controlling after TG1-EM1 resolves will be destroyed by Smashing Ground if it's the only face-up monster you control. If you're controlling another face-up monster with higher DEF, it will be destroyed instead. As noted before, Smashing Ground does not target, and in this situation, the Warwolf will remain on your opponent's field unharmed.

Because the monster is chosen at resolution not at activation.

The monster isn't chosen at all. The monster with the highest DEF instantly goes at resolution.

Smashing doesn't target becuase it searches the field.

Quite simply:

CL1: Smashing (Warowolf)
CL2: TG1-EM1 (T-King for example)

Chain resolves backwards.

CL2 TG1-EM1 resolves, netting you a T-King and your opponent a warwolf.

CL1 Smashing resolves, destroying T-King (given it had the highest DEF).
Smashing still goes after your opponent's side of the field, regardless of what switches.