I'd like to answer your questions honestly. You may feel that the answers are pessimistic, but I assure you they are honest.
I have a MSCE with emphasis in structural. I have 28 years experience and can do nearly everything in structural engineering such as structures, foundations, seismic analysis, dynamic analysis, finite element analysis, etc.
Many people will tell you things are great when they are not. Often, they are in denial. However, your query demands an honest answer.
1) Job/career stability?
When I started in this field, layoffs were rare. Typically, once you became established at a company where you fit in emotionally and professionally, you stayed for life and retired with a good pension. Now, layoffs are common and retirement parties rare. Industries in this country are closing and the production (and engineering) are going overseas. This trend is increasing with no end in sight.
2) Likelihood of getting on with State DOT
If you're right out of school, there is a reasonable chance of getting a job with a DOT. They are generally good, stable jobs. Gaining employment later in your career is not likely unless you know someone in an infuential position.
3) Do structural guys and gals get on as city engineers?
In large cities, occasionally entry level positions open up. These are generally stable jobs. However, pay is usually low and advancement slow. Towns and smaller municipalities typically buy their services from a local civil engineering company. With these small companies pay is usually low unless you are a principal in the firm.
4) Would you do it again if you were starting out?
No. When I started out the business, pay and opportunities were great. But now I wish I had become a doctor. I started with a company that had been in business for 85 years and had NEVER laid off an engineer. I have had 3 jobs in the last 2 years. And I'm lucky to be employed many of my friends (also engineers) aren't.
5) Any other emphases that should be studied in parallel ?
Soil mechanics. Often you have to estimate a project before the soil report is finished. Also, you will often use an old soil report which doesn't give you the spectifc soil property you need, or didn't take a boring where you would like it and you have to make a judgement.
I'm sorry if this dampens your enthusiasm. But, if I were you, I would persue another career. If trends continue (and there is no reason to believe they won't) structural engineering will not provide you with the monetary or emotional rewards you seek.
I wish you luck in your decision.