Galad's most likely too old to be a sparker.

The "oneness" is not only a trick to embrace the Source, it's a state of mind used and taught by blademasters and other martial arts practitioners (it also exists for real, btw). Tam taught it to Rand. Lan uses it too. So does Galad who was taught it by Bryne etc. Nothing in the scene you quote suggests Galad was embracing the Source. He achieved the Oneness, that's all, and as Rand also does to embrace the source, this is where the similar description of the state of mind came from.

Gawyn has much better odds of being able to learn to channel. I don't remember for sure how the genetics of channelling works, though. I think at least one of the parents must have the dominant gene, but I'm not sure.

Gawyn seems to have better odds, as his mother and father have produced another child who can channel. As for Tigraine, she couldn't even learn to channel (she's Tower trained, remember. If she could channel, the AS would have found out), so it's fairly obvious Rand owes his ability to Wise Ones or latent male learners (or both) in Janduin's near ancestry. Janduin could very well have been the son of a Wise One and have been a potential learner, for all we know.

As for Taringail, it's hazy at best, since his mother wasn't even Moiraine's. There's no one we know in the Cairhienin royal line but Moiraine who can channel - everybody else would at best be latent learners, so it's quite possible she got her ability from her mother's side (who was an odd match for a high ranking Cairhienin noble like Moiraine's father, IRRC).

I guess there's a fair chance that it comes down to:

Morgase (channeller) + Taringail (?): can produce a channeler
Janduin (? - but forcibly has channellers in his near ancestry) + Tigraine (proven non channeller): can produce a channeler
Tigraine + Taringail: can't produce together a channeller.

But someone who remembers the genetics of channelling as Jordan explained it will be able to tell you better.