More or less deal with the use of prepositions

Hi. I believe the questions I am about to ask have the use of prepositions as part of their elements. (I am not sure I asked correctly to reflect what I wanted to say, though.) Please help.

1. When do we use the phrase "continue something" and the phrase "continue with something"?

eg,

continue with the discussion

and

continue the discussion

2. Could we use the phrase "at the door or the range" to mean "very near the door or the gas range"? I think they don't mean the same, though, but I want your help.

eg,

stand at the door/gas range

I think we could write, "sit at the table" to mean "eating at the table" (not sure, though)