I would most likely use "Hej" or perhaps "God dag" when talking to an adult. To new youngsters coming to their first table tennis practise I tend to say "Morsning", but "Hej" would definitely word there as well.
Usually I only use "God morgon" before having my breakfast (e.g. greating people in the lobby when going to the breakfast room in an hotel/hostel) and then I switch to "Hej" / "God dag" when I've finished my breakfast. Sometimes I use "God morgon" in the evening and "God kväll" in the morning with people I know simply because it's fun to see their reaction, but I wouldn't advise doing that with people you don't know... :-)
I usually only use "Hallå" when talking on the mobile phone and the connection starts breaking, but there are definitely regions in Sweden where "Hallå" is the most commonly used phrase for greeting (and in those regions you will be greeted that way even in shops and restaurants).
"Hej" is used more or less in the same way you would use "hello" in English.
"Hallå" is usually (except for the regional differences mentioned above) used as a call-out ("Hallå" <-> Hey you, "Hallå där" <-> Hey you over there) or when you're checking whether someone is in a dark room or a seemingly empty house.
Some also use "Hallå" when answering the phone, though it's definitely not as frequent as the German "Hallo" or the English "Hello" in this kind of situation.
Not really much of a difference (but the word usually ends with a 'n' in Swedish). "Och" is usually pronounced "o", which is why it might be hard to hear.
You might also hear the version "Gomorn o välkommen" in some parts of Sweden (not really sure of the area separation, but I'd say that "gomorn" or "morn" would be the versions you're most likely to hear within a 150km radius of Gothenburg - so around 10% of the Swedish population would use those versions).