I didn't have the patience to read everything that everybody had to say, so please excuse me if I repeat something. I'm not an expert on this subject, but I do work with navy divers all the time, I've been active duty in the navy for the last 9 years, so maybe you can take something away from what I have to say.
First off, all recruiters are the same, they lie, bs, distort the truth, and tell you what you want to hear to get you to sign up....why? it makes them look like they're doing their jobs....unfortunate, but true.
As for the seal training, you'll probably be asked in bootcamp if you want to try out. This meant waking up 2 hrs before everyone else (0230) to go pt with the seals for a few weeks. If you pass their test, from what I hear you'll be given a chance to go to seal training, only after you pass bootcamp and your rating school. If you've been picked up for the nuclear field, you are SOL ofcourse....nukes cannot apply, due to their job requirements.
If you really want to become a navy diver before seal training, you can go through your rating school, report to your boat and request such a school, but it is not always guranteed and is based on the ships need at that time. For instance, most submarines train 4-5 people to become divers...(one or two nukes at the most.) If these billets are already filled when you report, you're SOL till one of them leaves. And even then, your primary job will be your original rating and not diving. You will only dive when the ship is leaving port, and it is your turn to (amongst the rest of the divers). Now...This might be different on a surface boat, but that's just from my experience.
You can always request SEAL training....from what I hear, they're hurtin for more people....
and for the security clearance thing, I thought you recieved your citizenship when you serve in the US military?
I'm a naturalized citizen myself....had to get a waiver to come into the nuclear program.....and I've had upto a "secret clearance" with no problems...it's really based on a "need to know" from then on....but it shouldn't be a problem.
remember....talk to the guys that are in the diving program...the seal teams...or the navy....don't ask the recruiters anything...they'll just tell you what you want to hear.
hope it helps....
and to address the laser eye surgery thing, I've heard that it disquals you, due to the outer flap of your eye potentially bubbling up when you ascend........unless you do PRK which is a method in which they just shave the outer layer off....(I know a diver that's had this done...and he said it hurts...alot..)