Hi virus_n00b: great questions but no, your statements are not correct. Here are some suggestions on how to think about phylogenetic trees.
There are nodes that are either terminal (your data sequences v1 to v11) or internal (inferred ancestral sequences; some software packages allow you to see these inferred sequences, while in your tree they are indicated as solid orange circles). The tree may or may not have a node at the top (the "root") which is the inferred ancestral sequence. In your case it appears that the tree is rooted, with the root placed as an orange circle along the left-most margin halfway down the page.
Every phylogenetic tree is defined by just two main properties: the branch lengths and the topology. I suggest you consult an article or textbook that explains this. For a great, brief article that explains some of the concepts in my response see Baum et al. (Science, 2005), "Evolution. The tree-thinking challenge" (PMID 16284166). In terms of your tree, I recommend that you use a software package (such as MEGA) that defines the units along the x-axis (e.g. number of amino acid or nucleotide changes per site, or time).
A clade is a group that contains any subset of your sequences (e.g. v2+v8) and their common ancestor, without excluding any descendants from that common ancestor. So the clade containing v2+v8 (what you called a sister group) must also include the common ancestor of those two sequences, which is not labeled but is given by the orange circle. A clade containing v2+v8+v6 must also include v5 and the three orange circles at the upper right of your figure.
If you add variant 1, your clade now has v8+v2+v6+v5+v1, and the common ancestor of this group is the orange circle from which all these five variants descend, and also including the three ancestral sequences given in orange circles at the upper right. Thus your statement that variant 1 is ancestral to v2,v8,v6, and v5 is definitely not correct.
You wrote: "v11 is ancestor for v9, v10, v1, v2, v8, v6 and v5". No, again, v11 cannot be the ancestor: the orange circle that connects to v11 is the ancestor of both v11 and v9, v10, v1, v2, v8, v6, and v5.
You wrote: "v3 is ancestor for v4, v7, v11, v9, v10, v1, v2, v8, v6 and v5". Here the situation is more complicated. Most phylogenetic trees are bifurcating: each node has two descendant branches. Here your tree is multifurcating which means it is not resolved. This is not necessarily a problem but means you need to be even more cautious in defining ancestors.
Always be sure to use a high quality multiple sequence alignment as input. If you select random sequences you'll still be able to make an MSA and a tree, but it won't be biologically meaningful.