I'm turning your Q backwards a little to see if I'm right?
When will my son:
- Dress himself always
- Ditch the lovey
- Stop whining
- Stop crying
?
Not for several years to come.
(Ahem...And many grown men have difficulty dressing themselves! But boys in particular tend to like to go about half dressed, not dressed, or inappropriately dressed).
It's all about the AMOUNT of time he spends doing each that determines whether this is perfectly normal development, or whether there's an issue. For example... many teens and even adults still have a stuffed friend or special blanket. They just leave it at home! But go to a children's hospital, and their loveys all come with them. From toddlers to teens. Go to any college campus and you'll find teddy bears in dorm rooms. Most parents, when they have their children, still own a favorite friend from childhood that they may or may not pass down.
So it's normal to have loveys. Throwing a screaming tantrum at age 4 if he's separated from his lovey even while in the wash isn't normal. Sitting and staring at the washing machine IS normal. So is not particularly caring if his lovey is having a bath. There's a wide range of normal.
Also what you're doing to encourage or discourage, and what your expectations are (for example; even an adult will break down in tears when they're exhausted and haven't eaten all day... a kid will do it after "just" a few hours)... play a part as well. Many parents encourage whining and tantrums, because they can't stand whining, so the moment the child whines (or 10 minutes of whining later) the kid KNOWS they will get what they're whining for. Whining works in those situations, so there is no reason to stop, and every reason to whine as much as possible. But even kids who almost NEVER whine... will whine when they're scared or tired. An adult who never whines will wine when pushed past their limits, too.
So there's a huge variation, and none of these behaviors ever just "stop", although they decrease or rarely happen as long as you can stay on top of a lot of them...but no one can control the world. Kindergarteners often start behaving like toddlers; for the pure and simple reason that they use up all their self control at school, and come home exhausted. TOTALLY to be expected. It's part of why most families schedule nothing for directly after school... so their kids can eat and rest. Other families, their kids are fine, and they can dive straight into homework or an activity/sport. And a family will often have one of EACH kind of kid!
If you're worried, though, get an eval :) The #1 that something is off, is a parent's instinct that something is off. Sometimes parents just have unrealistic expectations. So no matter what, an eval helps. Either the kid gets help, or the parent gets help. Win win.