It pays well over average for most majors, it pays above average for STEM degrees, and it’s reasonably possible to find a job. There is absolutely no guarantee to find a job, much less a great job, upon graduation.
No. It’s miserable if you have no love for it at all. Though perhaps if you have a moderate but not strong interest, it’s not a bad choice.
It is an issue, it has always been an issue, and it will continue to be an issue for the foreseeable future. Engineers are not alone in suffering from this - other professionals who work on the kinds of projects engineers work with (a lot of people) suffer from outsourcing as well. Automation is another reason - automate a task, you no longer need as many salaries workers (engineers included) to maintain it. Foreign H1-B workers are another concern - more competition for jobs. And so on.
It’s not a field without its problems, to put it simply. A lot of people are overly optimistic about how things are going, because it is indeed better than average, but these problems do exist.
Hopefully. You’d be surprised though. I’ve been amazed before at how bad some engineers are at basic skills like physics, math, and especially writing. Some people get tunnel vision after some years and stop being all that well-rounded.
It’s very common that people land far from where they started, career-wise. Engineers are no different.
And to answer the title of the thread:
“Engineering” is no more a single field than “business” or “science.” It’s a field with a lot of different sub-fields, each with their own markets that are either in recession or in a boom. Computer science, especially certain hot subfields like social media and related subjects (websites, data mining, etc.) are in a boom. Civil engineering is in a bit of a recession, still recovering from the real estate crash that happened a few years ago. Petroleum is suffering from the crash in the oil prices. A lot of the big infrastructure fields are suffering from outsourcing. Defense contractors are doing pretty good (they fell into a real rut at the end of the Cold War). I could go on…
So, basically it’s a market.