First Question - yes.
Second - The perks on the right hand side of the tree (inc the first Shield Wall, all 5 levels), Quick Reflexes, Power Bash, Deadly Bash and Disarming Bash are the only ones relevant to two-handed weapons. The left side of the tree is strictly sword & shield
stuff.
Do note though when you're using your points the Two-Handed Power Attack perks are your most important IMO for two-handed weapons. Invest in Stamina and power-attack as much as you can and you'll carve it up. Blocking is still very useful and worth the points
if you want to invest in them BUT prioritise on your Power Attacks.
Note also if you're gonna use the Bash perks in blocking you also need stamina.
So if you're a two-handed specialist (and I've got one) - put most of your points in stamina, some in health, and (if you need it) even less in Magic.
My bloke relies on Restoration magic for healing (don't like carrying thousands of potions) so I run a percentage of 3 (Stamina), 2 (Health) and 1 (Magic) BUT when he gets to a level high enough to do me I'll be dropping investment in Magic completely and
just concentrating on Stamina, Stamina, Stamina and Health.
Go bash some brains in.