One question about dex characters and rogues, is there any reason they can't use a shield?
There's nothing prohibiting Rogues from using a Shield.
Only thing you miss out on is making use of Thief's additional bonus action for extra off-hand attacks (Which is often the main reason to actually play Rogue in the first place).
Shields don't provide any innate penalties to a character though, unlike Heavy and certain Medium armours which provide a disadvantage to Stealth skill checks. So you're perfectly capable of sneaking around with a shield. (That said, you're also perfectly capable of sneaking around with Heavy armour too as stealth checks are only done when you're visible and in someone's vision cone... So utilizing the plethora of ways to get invisibility or just not walking in anyone's vision cones completely bypasses the stealth skill entirely)
