1 - We're just distant relatives.
2 - We're close relatives.

or

1-We're just distantly relatives
2-We're closely relatives. это звучит нормально?

Distant
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"Distantly" is not a word.
"We're just distant relatives." - would be correct.
"We're distant relatives." - the "just" can be omitted, unless you're really trying the stress an unimportance of your relation to the other person because of how distant it is.

Close
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"We're close relatives." - though this could also imply relational closeness, instead of genealogical closeness.
"We're closely related."
"We're related." - the close could be omitted unless you are trying to stress the closeness of your relation

Immediate
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"We're immediate family." - typically just spouse and children (for insurance purposes), but otherwise includes parents (the children's grandparents).