'well' can be used is a lot of slightly different ways.....but it usually indicates there is no clear cut answer to the question asked. What time is the bus coming Julie?: "Well, the timetable says 7pm but the lady at the kiosk said there might be delays"

In your examples, and often at the beginning of a sentence, "well" isn't really a word at all. It doesn't have any meaning. It's just a "filler." It's a kind of noise that means "I'm thinking about what to say next." It's like "Um" or "Ah" or "Hmmm." Everybody uses fillers, everybody--but in public speaking courses they try to teach you NOT to use them. Fillers are a way of saying "I want to speak, even though I don't know what to say yet." It's not a good speech habit. Notice how ahdictionary.com explains this use of the word. It simply says how it is used--it doesn't try to say what it means, because it doesn't mean anything. "interj. 1. Used to introduce a remark, resume a narrative, or fill a pause during conversation. 2. Used to express surprise."

Well, I was going to answer this question, but I see you already have answers. :D

I can't resist mentioning this. But I'm making a joke. Here is the ULTIMATE lesson in how NOT to use the word "well." Believe it or not, in 1963 this song became the #4 song in the United States. The lyrics consist of almost nothing but the phrase "bird is the word" plus the filler word "Well:" A well a everybody's heard about the bird B-b-b bird, bird, bird, b-bird's the word A well a bird, bird, bird, bird is the word A well a bird, bird, bird, well the bird is the word A well a bird, bird, bird, b-bird's the word... https://www.youtube.com/watch?v=QXLqMB6vBic