Are there NPC enchanters and smiths in the game who sell their services or is the only way to get a personalized enchantment or improved equipment to do it yourself?
No NPCs offer it. You will find enchanting tables, alchemy tables, tanning racks, grind stones, smelters, workbenches and forges to do it yourself. The focus is very strong on DIY. You hunt a deer, take its fur and turn it into leather and leather strips at a tanning rack, and make an armor of it at the forge and improve it on a workbench. Smelters are used to turn ore into forgable metal ingots.
Also, are there enchanters who you can pay to recharge your weapons, or do you just have to buy the soul gems and do it yourself?
You can buy and find soul gems to recharge enchanted weapons. No NPCs offer a service to recharge it for you.
When is the main questline activated?
It is kind of always activated, but there is no time preasure and besides one single dragon will there be no other dragon attacks until you have passed a first few simple stages of the main quest.
Are dragons present from the start no matter where you go first, or is there a trigger (like with Kvatch in Oblivion)?
Only one dragon as part of the introduction. See above.
Furthermore, does the world suddenly know I'm Dragonborn upon absorbing my first dragon soul, or is it a particular dragon soul that triggers it?
People will say something when they see you absorb a soul, but it is only comments with no consequences to it. A recognition by officials happens in the main quest and it is the same part after which the dragon attacks will start.
Once I escape Helgen, must I follow one of the two men to Riverwood, or can I just abandon them?
No. You can follow them but you do not have to. You can go anywhere you like.
I'm sure I'll think of some more questions in the near future. When that happens I'll post them here.
Just get the game. It is Game of the Year. Many people got it and everyone loves it. So much that they want more and complain about everything.