I have had 4 P226's (2x 9mm, 1 357, 1x 357 with rail). My answers to you questions are as follows:
1. my definition of shooting fine is as follows: very reliable, accurate enough for their intended use and a trigger good enough to allow me shoot the weapon at my normal level of accuracy. If your definition of "shoots fine" is similar, you will need no work on the weapon
2: Yes, two of them have been to Teddy Jacobsen. He did a great job, made what was already an acceptable trigger into a really smooth trigger and polished up all of the insides. He is partially retired now and is not taking in much work, and I do not have any other suggestions.
3. in my opinion, no other work, other than maybe night sights is necessary. They are extremely reliable out of the box, are accurate and shoot well.
3A. Although not asked, if you have work done, never let a gunsmith cut down the springs (hammer,etc) of a Sig-Sauer. If someone claims that the trigger pull can be lightened by trimming some coils off of the mainspring, never let them touch your gun.