1a. Two species that possess a homologous trait are frogs and lizards with their forelimbs. Frogs are amphibians that mostly live near moist wetlands while lizards are reptiles that live in more dry regions.
1b. The forelimbs of a frog are used for a multitude of things, but most notably for locomotion (both land and water), balance when standing/sitting and absorbing shock from high impact stress on the body.

The forelimbs of a lizard are used almost strictly for locomotion on land, however, there are other lesser known uses for them such as hunting, scavenging and feeding.
1c. The common ancestor between these two had to have been some sort of large reptile. When part of the population was forced to live near large masses of water, it adapted its forelimbs to accommodate the change in environment.
2a. Two species that share an analogous trait are humans and octopi. Both species use eyes for seeing, but both sets of eyes have adapted for completely different environments.
2b. Human eyes are used only for vision. They are adapted mostly for environments where sunlight or some substitute is present. There is a clear periphery where vision gets blurred and blind spots where the eye cannot see due to placement on the human.

Octopus eyes are also only used for vision. However, they are adapted for the deep sea where there is not sunlight. Also different from humans is that they do not have a blind spot, meaning that they can see everything around them.
2c. The common ancestor between these two must have the analogous trait because both of the structures are used for the same thing (vision), however they act different because they are adapted differently to their respective environments.