Hey monkey
A reasonable mechanism for the first reaction could be as i have shown in the jpeg attached. Deprotonation of the phenolic-group (acidity of the hydrogen is provided by resonancestabilization of the anion formed) and then attack by the nucleophilic oxygen on sulphur in the triflyl-group giving the product and a secondary sulfoneamide.
The first step in the mechanism of the second reaction is an oxidation with hydrogenperoxide under basic conditions. The mechanism for this reaction can be found in any organic chemistry textbook, just look under hydroboration/oxidation. The product of the oxidation is two phenolic-groups. A rearrangement provides the product shown (se jpeg attached)
Rico