Well no, they use boats, not plane. ;-)

But mostly yes. It is interesting to read a bit on submarine cables that our infrastructure depends that much on.

It is for instance interesting to know that their landing points are considered strategical locations and that at least US and Russian navies have trained at eavesdropping on them using submarines. Just throwing that in case you are wondering why you don't hear much about X-37's ability to rendez-vous and "repair" satellites.

Mostly yes, they do protective measures like burying in highest risk waters.

(The surveying involved in route planning prevents dangling the cable in nonworkable ways)