To answer your questions,
1. Until the final rule is out and all the aviation colleges and flight schools have lobbied for their special exemptions and cutouts to the ATP rule, there's no way of knowing how being 23 will effect your ability to get hired at a regional. In the mean time, build time as a CFI, do some right seat corporate stuff, fly for a part 135 outfit. The opportunities in aviation are endless. Spend your summers pumping gas at the local airport. You'll find out what's out there real quick.
2. Depends. I went to school with a guy who interned at Continental in college. He got some RJ time and got hired at CAL when he was 24. I refer to him as Number One. I'll let you figure that one out on your own. A lot of people have been hired by the majors in their 20's. The current hiring climate has more to do with if you can get hired than your actual age.
3. Again, depends. It's always better to be well-connected than good in my book, but connections may not carry any weight at some airlines until after the interview (SWA comes to mind). I know one guy I used to fly with who's dad was a super-senior check airman FedEx captain. His dad's pull got him an interview, but he didn't get hired (his entitled arrogant attitude MAY have had something to do with that).
4. Will this be a good career path in the future? Wow. Wish I had the answer. A lot of it is what you make of it, but sometimes things just don't pan out. A fellow CFI and I got on at the airlines during the same month. We have worked for two of the same airlines along the way. I have been flying heavy jets internationally for 4 years, he just got downgraded to FO on a turboprop making less than 30k a year. VERY similar career paths. Ask us each if it was worth it and I bet you will get two different answers. I hate to use the word luck, so I will use the word timing. Sometimes, timing sucks. Somehow, I have a feeling that you will be just fine if you choose this career field.
I applaud you for your early commitment to a challenging and rewarding career path. Keep focused on reaching your career goals, but be open to learning about your strengths, weaknesses, skills, likes, and abilities inside AND outside aviation.
For example, if you are itching to get a rating, I believe you can take your Private Pilot-Glider on your 16th birthday (and solo NOW). It will be a LOT of fun, and the skills you will pick up will make you a better pilot overall. Do your private in a taildragger. Fly into grass strips. Do lots of cross-countries (50NM+ to count towards the Instrument Rating).
I also learned I really enjoyed teaching when I went through my CFI course. Sure, I did the CFI thing for a few years, but the teaching and CFI background led to a Check Airman position at my former airline, which led to a 757/767 job at my current employer, which led to some part-time sim instruction for another 121 carrier.
The doors that have opened for me and the opportunities I have had are not NEARLY what I though they would be (9/11, financial crisis, $140/bbl oil), but they have been more diverse and fulfilling than I could have imagined when I got my Private at 18. DO I work for a Major? No. Have I seen the world and flown some incredible aircraft? Yes. I wouldn't trade it for anything.
I apologize if I am rambling, but seeing someone your age with the ambition and opportunity you have is encouraging, even exciting. I think a lot of us on this forum were in your shoes once, but perhaps lacked the capital resources to make things happen at 15. Study hard, fly safe, enjoy your remaining teen years, go to college, and fly a little bit, too. Just realize you will only get out what you put in, and nobody owes you anyhing in this business.
And one more thing, start taking the time to invest in others if you aren't already. Volunteer. Make a difference in someone's life along the way.
All the best,
Dog