User blog:Edwin Shade/Ordinal Questions

In the near future I would like to write a blog post which lists all the significant ordinals known to date and why they are important. I have some questions though, and I believe it's best they are all gathered together in one blog-post for efficiency. I may add new questions occasionally.

1.) Is there a special name or symbol used to denote the ordinal infinity corresponding to the cardinality of the real numbers, \beth_1 ?

2.) More generally, is there a notation for ordinals which corresponds to an ordering of $$\beth_{\alpha}$$ elements within a set ?

3.) If the continuum hypothesis may be assumed without contradiction, does that mean the plane can be filled with an $$\aleph_1$$ amount of lines with no gaps ?


 * 3.5) If the continuum hypothesis may be denied without contradiction, does that mean the plane cannot be filled with an $$\aleph_1$$ amount of lines with no gaps, and hence the question overall is undecidable ?

4.) If the continuum hypthesis may be assumed without contradiction, does that mean you may consider an n-cube a visual representation of the ordering $$\omega_1^n$$ ?

5.) The ordinal which corresponds to the ordering of the aleph fixed point $$\aleph_{\aleph_{\aleph_{._{._{.}}}}}$$ is $$\omega_{\omega_{\omega_{._{._{.}}}}}$$. What is the name and symbol for this ordinal ?

To those who are able to answer these questions, or at least one of them, thank you for your help.