Will osteopenia eventually develop into osteoporosis?

Not necessarily. "osteopenia" is not a disease. It's a level of bone mineral density (bmd) that was literally invented due to being near but not as low as the osteoporosis bmd selected by the who in the 1990s. The fact is that some people with the "osteopenia" level bmd have more risk of fracture than others who meet the "osteoporosis" definition. Please, ask your doctor for a clinical risk frax analysis!
No. Patients with osteopenia need to make sure they are getting adequate calcium and vitamin d intake (through diet or supplements), stop smoking and increase their weight-bearing exercises. Doing the above will strengthen bones and prevent progression to osteoporosis.
Probably. Osteopenia will likely progress to osteoporosis without aggressive preventive measures such as weight bearing exercise, calcium, vitamin D and perhaps bisphosphonates.