modelsim compiling error:external function 'xxxxx' may not be used in a constant expr

This worked for me going back a number of releases. You have a few typos. Make sure what you posed is exactly what you are compiling.

package pkg;
function bit bitgen(int bit1idx);
    automatic bit res = '0;
    if (bit1idx >= 0 && bit1idx < 16)
        res = 1'b1;
    return res;
endfunction
function bit bit2test(bit bits2test);
    if ((bits2test&bitgen(2)) != 0)
        return 1'b1;
    return 1'b0;
endfunction
endpackage
interface iftest# (
    parameter para2test = 15
);
    import pkg::*;
    localparam bit2set_flag = bit2test(para2test);   // modelsim reports compiling error here!
    initial begin
        if (bit2set_flag == 0)
            $error("bit2 of para2test is not set!");
    end
end
module mod2test# (
    parameter para2test = 15
);
   import pkg::*;
    localparam bit2set_flag = bit2test(para2test);   // the code here passed modelsim's compiling
    initial begin
        if (bit2set_flag == 0)
            $error("bit2 of para2test is not set!");
    end
endmodule

You still have typos. This works for me after replacing end with endinterface.

Yes, without the static or automatic keyword, it is difficult to know if the local variable gets initialized once at time 0, or each time the function gets called. I think its best to declare your package as automatic, then all the functions are automatic, and all the local variables inside the functions are automatic. Then, only declare local variables as 'static' when they need to be.

automatic package pkg;
// ... dummy codes...
endpackage

Let's say you have this

package pkg;
int gacc;
function int fout(input int in);
  int acc;
  if (in !=0) begin
      acc += in;
      fout = acc+ gacc;
      gacc = acc;
  end
endfunction
endpackage
// in some code you have
$display(fout(1)); // prints 1
$display(fout(0)); // prints 1 - returns last value assigned to fout
$display(fout(1)); // prints 3

package pkg;
int gacc;
function automatic int fout(input int in);
  int acc; // implicitly automatic
  if (in !=0) begin
      acc += in;
      fout = acc+ gacc;
      gacc = acc;
  end
endfunction
endpackage
// in some code you have
$display(fout(1)); // prints 1
$display(fout(0)); // prints 0 // no value assigned to fout
$display(fout(1)); // prints 2

package automatic pkg;
int gacc; // always static - not inside any block
function int fout(input int in); // implicitly automatic
  int acc; // implicitly automatic
  if (in !=0) begin
      acc += in;
      fout = acc+ gacc;
      gacc = acc;
  end
endfunction
endpackage
// in some code you have
$display(fout(1)); // prints 1
$display(fout(0)); // prints 0
$display(fout(1)); // prints 2

Wow, it seems that the automatic package is just the feature what I want!. will it damage or impact the type definition in package?

package automatic pkg1;
    typedef enum {
        t1 = 0,
        t2 = 1
    } type_t;
endpackage
package pkg2;
    typedef enum {
        t1 = 0,
        t2 = 1
    } type_t;
endpackage

It has no impact on typedefs. It only affects the lifetimes of variables declared inside named blocks, functions or tasks.