Q1.
Since convex lens converges a light beam, can it also burn a paper?
Answer
Yes. Anything that concentrates sunlight into a small enough spot can char and ignite paper, and a convex lens converges light just as a concave mirror does.
The only difference is the route the light takes. The concave mirror sends the sunlight back to a focus in front of itself; the convex lens lets the sunlight pass through and brings it to a focus on the far side. In both cases the energy falling on the whole face of the mirror or lens ends up on a spot a few millimetres wide. Activity 10.11 is exactly this test.
Safety first: never look at the Sun directly or through the lens — it can damage your eyes permanently.