While it's true you can't hire an npc to create an item for you(smithing) or improve an item for you(smithing or enchanting), there are merchant trainers. In vanilla Skyrim, there are several smiths you can pay for training and then sell them stuff to get your gold back. These include Gorza in Markarth(common trainer up to level 50), Balimund in Riften(expert up to level 75) and Eorlund in Whiterun(master up to level 90). The Dawnguard adds Galmar(master at Fort Dawnguard) and incidentally Sorine is a master archery trainer and merchant(same location). That isn't so relevant but it adds to getting free training with Faendal at the start of the game and with members of the circle once you are harbinger. If you have high alchemy skill and perks, it helps to sell potions and poisons to merchant trainers to get your money back.
For Enchanting, only Sergius Turrianus of the College(expert) and Hamal in the Markarth Temple of Dibella(master) are enchanting trainers in vanilla Skyrim, but neither one is a merchant(and Hamal requires a potentially dangerous quest be completed before becoming available). If you have the Dragonborn DLC, Neloth at Tel Mithryn on Solstheim is a master enchanting trainer and a merchant. On a side note, his apprentice Talvas is a master conjuration trainer and merchant who can also be your follower as well.
With patch 1.9, you can make any level 100 skill legendary, resetting the skill to 15 and refunding the perk points you spent in it. You can level the skill again for more xp to raise your character level, get more perks and more attribute increases. A skill can be made legendary as much as you want, removing the previous level cap of 81 and allowing you to get all perks in every tree if you want to. The easiest without exploits are either Alteration(telekinesis fast travel between Riften and Markarth) or Illusion(cast Harmony in a crowded place like the Riften market during the day. May help to be thane wherever you try this so guards don't get on your case). Both methods benefit from having a set of gear making spells free to cast(totally doable with 100 enchanting, relevant perks and grand soul gems). You can even freely cast 2 spell schools with one set of gear with the level 100 enchanting perk Extra Effect. Hope this helps.