There is a continuing debate on whether the project manager needs to be an SME (specialist) in his field or not (generalist). So no one can give a definitive, objective answer to your question.
Now let me answer your other questions:
1 - I think it's excellent to have a degree in construction - it will help you become a construction project manager and it will help you secure a very high salary.
2- CAPM is a good way to enter the project management world, especially for helping you secure a low level position in PM (such as project manager assistant - PMA)
3- Job security no longer exists - both employees and employers are no longer loyal to each other (in the old days, one could work for 30 years for the same company without quitting or getting fired - now that was job security). I advise you to get into the construction industry, lots of work worldwide and higher salaries than other professions.