1. Thiosulfate is unstable under acidic pH conditions, causing the thiosulfate to decompose into sulfur dioxide, elemental sulfur, and water. Sodium carbonate in solution is alkaline, and the abundance of hydroxide anions prevents the thiosulfate from encountering the positive charges that would trigger its decomposition. So, sodium carbonate can be used either to stabilize thiosulfate, or to lower its reaction rate with anything else that it's been combined with.
2. Thiosulfate titration can be an iodometric procedure. Iodometry involves the use of iodide (the iodine anion) to indicate the presence of an oxidizing or reducing agent. Because elemental iodine is highly electronegative, it will tend to draw one of the two extra electrons in the thiosulfate to itself. This reaction can be combined with others, such as starch indicators, making the thiosulfate reaction an intermediate to determining the properties of an entirely separate compound, or used with thiosulfate alone to determine the concentration of thiosulfate in the solution.