'CurveIntersections' object has no attribute 'Item'?

sure, here’s how you should use the code

import rhinoscriptsyntax as rs
import Rhino.Geometry as rg

a = []
b = []
for curve1 in curves:
    for curve2 in curves:
        if( curve1 != curve2):
            itxn = rg.Intersect.Intersection.CurveCurve(curve1, curve2, 0.0001, 0.0001)
            #count=getattr(itxn,'Count')
            #print(count)

            #this is how you should ge the number of itersection
            count = itxn.Count

            #this is a standard loop in pythin
            for i in range(count):
                #gets the intersection event
                ix = itxn[i]
                a.append(ix)

                #gets the intersection point - there's more to this
                #check https://developer.rhino3d.com/api/rhinocommon/rhino.geometry.intersect.intersectionevent
                b.append(ix.PointA)

@Xusheng_Li note: there’s a problem with your outer loop logic, that’s why it returns extra points

use this pattern or similar

for i in range(listLength - 1):
    for j in range(i+1, listLength):
        #intersect curve[ i ] with curve[ j ]

updating the code above

# this takes intersection of all curves and build geometry around the intersection
# input type: curves - Curve (List Access)
import rhinoscriptsyntax as rs
import Rhino.Geometry as rg

a = []
b = []

curveCount = len(curves)
for k in range(curveCount - 1):
    for m in range(k+1, curveCount):
        curve1 = curves[k]
        curve2 = curves[m]
        if( curve1 != curve2): #this is redundant now...
            itxn = rg.Intersect.Intersection.CurveCurve(curve1, curve2, 0.0001, 0.0001)
            #count=getattr(itxn,'Count')
            #print(count)

            #this is how you should ge the number of itersection
            count = itxn.Count

            #this is a standard loop in pythin
            for i in range(count):
                #gets the intersection event
                ix = itxn[i]
                a.append(ix)

                #gets the intersection point - there's more to this
                #check https://developer.rhino3d.com/api/rhinocommon/rhino.geometry.intersect.intersectionevent
                b.append(ix.PointA)