Which reactions are most common in alkenes?

$A$ benzene derivative did not produce a white precipitate with ammoniacal silver nitrate solution (Tollens' reagent) but decolorized cold dilute alkaline $KMnO_4$ solution (Baeyer's reagent). The compound is:

Ozonolysis of the given compound yields:

Write a test to detect the presence of a double bond in a molecule.

Out of the following,the alkene that exhibits optical isomerism is

Addition of $HBr$ to propene yields $2$-bromopropane,while in the presence of benzoyl peroxide,the same reaction yields $1$-bromopropane. Explain and give mechanism.