Connected, path-connected, and quasi-components of unions of concentric circles

Let \(C_r\) denote the circle of radius \(r\) centered at the origin in \(\mathbb R^2\). Determine the connected components, path-connected components, and quasi-components of each of the following subspaces:

1. \[ S=\bigcup_{n\ge1}C_{1/n}\cup\{(0,0),(1,1)\}; \]
2. \[ T=\bigcup_{\substack{r\in\mathbb Q\\0<r<1}}C_r\cup\{(-1,0),(0,0),(1,0)\}. \]