Question

Is it possible to create a foreign key where type of the first column is bit but type of the referenced column is int?

Answer 1

No.

create table X
(
  c int primary key
)

create table Y
(
  c bit references X
)

Returns:

Msg 1778, Level 16, State 0, Line 1
Column 'X.c' is not the same data type as referencing column 'Y.c' in foreign key 'FK__Y__c__34C8D9D1'.
Msg 1750, Level 16, State 0, Line 1
Could not create constraint. See previous errors.

Also see the relevant section in BOL:

• The REFERENCES clause of a column-level FOREIGN KEY constraint can
  list only one reference column. This column must have the same data
  type as the column on which the constraint is defined.

• The REFERENCES clause of a table-level FOREIGN KEY constraint must
  have the same number of reference columns as the number of columns in
  the constraint column list. The data type of each reference column
  must also be the same as the corresponding column in the column list.