All of your questions depend on the watch. Cheapo watches depend solely on the phone or device they are connected to. While more expensive watches can be more independent. They will also be a bigger burden on your wallet as you pay for voice plans, network access and the like. These are often meant to take the place of a phone more than be a companion to one. For the companion style of device, yes it must be within so many feet of the device they are connected to, they usually alert you if they become disconnected and can have a wide range of features. I haven't seen companion types that connect to WiFi but they are probably out there, I would guess that some of the one's with data plans could just to cut down on data usage. As for casting to a speaker I haven't seen any that do that but it could be because I never look in that price range. Most people I know with one seem to use the companion style of device. They present small quick access to incoming notifications and reminders. Some can have apps like Facebook and Instagram, I'm not sure about Spotify, and some can allow you to reply to messages quickly from the watch. I can't think of a reason why a watch would be used to cast to a speaker if the phone is available, plus think about the screen size. They are conveniences. I think about it this way, I'm out and get a text "when are you coming home?" a watch would be great for saying "in 10 minutes" or "at 4:30" but would be really too much trouble for, "how do I get the computer to print out this picture from aunt June?" I wouldn't want to type out step by step instructions on a 1.5" screen. As for how long will the battery last that will depend on the watch. I mean no one can really answer that with any accuracy because everyone uses theirs for different things, just like phones, and the watch that gets Joe from rise and shine to bed may only get Schmoe from morning to the end of the work day.
Your best bet is to look around some online. Figure out what features you want, what your price range is, spend a little time on Google and YouTube looking at reviews and go from there. That's the only way you'll really be able to answer "Is a smartwatch really for me (you)?
To reply to this thread please create an account. It's free and only takes a few minutes to set up. This link will help you do that...
https://forums.androidcentral.com/ask-question/409154-join-android-central-community-new-post.html