Can’t enter Goldenglow sewer in Thieves guild quest “Loud and Clear”

There's no real reason to complete this undetected (except for personal feel-goodsies, perhaps). The mercenaries guarding this place are nameless, "Mercenary" NPCs, so I wouldn't worry too much about killing them.

That said, your best bet is the same way you go about undetected in general - strip naked (armor is noisy!), hit up the dark corners, and make sure to hold shift (the default) to go extra slowly.

Windhelm, Markarth, Solitude and Whiterun all have "influence" quests that each become available once you've done 5 of the randomly-generated jobs from Vex and Delvin in that city. Since jobs in Riften or cities you've already completed do not help your progress towards completing the influence quest, you can save before taking a job from Vex or Delvin and then reload until you get a city you haven't completed yet, if you feel so inclined.

Completing the influence quests unlocks fences in Markarth and Windhelm, but most importantly, each influence quest you complete increases the available gold pool of all fences in the world, up to 4000 once all quests are complete.

When you've completed all four influence quests, plus the main Thieves Guild storyline, you can become the guild master, receiving a significantly-upgraded suit of the guild armor you gained when joining.