I agree with Grace that "Who else knows of that?" sounds unnatural. The first option is okay, and I don't think it sounds colloquial. There is also a third option: "Who else knows about that?"

Yes, "surely" means "certainly" or "definitely." Like Jan Halstead said, "surely" in this sentence means "you must think I am crazy" or "you will definitely think I am crazy." In this case, you could use either "probably" or "surely." It depends how certain you are that people think you're crazy.

My daughter sang Christmas songs

Today is Saturday, the last school day of the week. Actually, my daughter went to school only in the morning because there is no school on Saturday afternoons.
This morning was a special one. The school organized a choir with the kindergarten pupils ("students" is less formal/more common). In France, from 3 to 5 there are 3 classes for children 3 to 5 years old : Petite, moyenne and grande sections.
My daughter attends the 'little section'. I'm not sure there is an equivalent in the U.S.? Kindergarten is from 5 years old, right?
Anyway, this morning was the day were when the little ones had to sing Christmas songs in front of their parents.
The kiddos had prepared this event for a while, rehearsed their lyrics and it should be really frightening exciting? nerve-racking? to see all the parents attending their performance in the school yard.
The teachers had set up rows of chairs in the school yard and small benches were installed right under a porch for the kids to sit on.
While all parents were sitting at in their our places, we were waiting patiently and a little anxiously our kids to show up.
The temperature was just above 3°C, so I was a bit cold but the sun was out and it helped us to bear the coldness.
The kids finally appeared wearing Christmas bobtail hats (I've never heard them called "bobtail hats." We usually say "Christmas hat" or "Santa hat") and wondering what this crowd was doing here.
They began to sing and I started to weep. I was so proud of my daughter, singing these French rhymes, considering her endeavor to pronounce words correctly.

http://www.lemonde.fr/idees/article/2016/12/02/francois-hollande-l-aveu-d-un-echec_5042140_3232.html

Yeah, these are both very casual ways of saying "I agree to do my part." I would probably say "Yeah, I'm in. I'll do my part." I noticed your sentences both said "whatever my part is" but it's not totally necessary. If I say "I'll do my part", that means I will help, but it doesn't necessarily mean that I know what I will be doing to help — or what "my part" is. I hope that makes sense.

Et j'ai remarqué que j'ai fait une erreur dans mon texte ! J'aurais dû dire « quand je suis arrivée ». Tout le monde fait des erreurs. :)

Moi aussi, j'avais ce problème-là quand j'ai arrivé au niveau intermédiaire, et la solution pour moi ? Je devais parler plus souvent. C'est tout ! La répétition m'a aidée de parler plus automatique, avec moins d'effort.