Yes, the LME is MUCH heavier than water. You are well advised to heat your water to dissolve the LME.. but turn off the burner while adding until, after a ton of stirring, you feel it is all mixed in. If you are not adding specialty grains or hops, you don't need to bring it to a boil.. ie, if you are using hop flavored malt.
But, usually we add more hops.. so when the LME is added in.. bring it to a boil and follow the recipe for hop additions.
However, another thought. If you do hop additions, you might want to consider adding the LME just before you turn off the flame.. at the end of the boil. the LME is sterile and doesn't need boiling to sterilize it. So, you can start the boil.. when it's reached, start your hop schedule. Then at the end of teh 60 minutes, you can then add the LME AFTER you turn off the flame. The wort is well hot enough to dissolve the extract and kill any known bacteria that would harm beer. Be sure to stir the heck out of it..
You will not have a problem doing it this way. Also, not everyone agrees with the late LME addition.. but, as the pro's look more into it.. they seem to all agree that it's a good way to go.. You also come out with a more true color to style.
Regarding to adding somethng to the secondary, I guess you could dry hop the heck out of it. However, there are some grains that are added to some IPA's that have a burnt flavor. I recently made one and, while it seemed overpowering initially, it mellowed to a very good brew after a month. There was a hint of burnt in the background.. which many folks judged as a winner. YMMV