I'll be delighted to get some help from the experts around here, regarding the following questions:

1) If we take the collection of all rank 2 groups. Does this collection countable? Unctountable? Does someone know about any work concerning putting a topology on the collction of all groups or maybe on the collection of all rank 2 groups?

2) Does someone know about works concerning estimations on the number of metabelian groups, or on their density in the collection of groups?

3) Does someone know about any works about estimating the density of groups satisfying some property? i.e.- given a family of groups defined by a property $X$ , what is the limit of $\frac{no. X}{no. grps}$ when the order becomes infinite?

Thanks in advance !