How to create Cognito IdentityPool with Cognito UserPool as one of the Authentication provider using aws cdk?

This is the way I managed to mimic the default configuration created through the aws console when you create an identity pool with a user pool as identity provider. It includes some other features apart from what you have asked (allows unauthenticated access and specify the password policy), but is easy to modify to your needs.

    const userPool = new cognito.UserPool(this, 'MyUserPool', {
        signInType: SignInType.EMAIL,
        autoVerifiedAttributes: [
            UserPoolAttribute.EMAIL
        ]
    });
    const cfnUserPool = userPool.node.defaultChild as cognito.CfnUserPool;
    cfnUserPool.policies = {
        passwordPolicy: {
            minimumLength: 8,
            requireLowercase: false,
            requireNumbers: false,
            requireUppercase: false,
            requireSymbols: false
        }
    };
    const userPoolClient = new cognito.UserPoolClient(this, 'MyUserPoolClient', {
        generateSecret: false,
        userPool: userPool,
        userPoolClientName: 'MyUserPoolClientName'
    });
    const identityPool = new cognito.CfnIdentityPool(this, 'MyCognitoIdentityPool', {
        allowUnauthenticatedIdentities: false,
        cognitoIdentityProviders: [{
            clientId: userPoolClient.userPoolClientId,
            providerName: userPool.userPoolProviderName,
        }]
    });
    const unauthenticatedRole = new iam.Role(this, 'CognitoDefaultUnauthenticatedRole', {
        assumedBy: new iam.FederatedPrincipal('cognito-identity.amazonaws.com', {
            "StringEquals": { "cognito-identity.amazonaws.com:aud": identityPool.ref },
            "ForAnyValue:StringLike": { "cognito-identity.amazonaws.com:amr": "unauthenticated" },
        }, "sts:AssumeRoleWithWebIdentity"),
    });
    unauthenticatedRole.addToPolicy(new PolicyStatement({
        effect: Effect.ALLOW,
        actions: [
            "mobileanalytics:PutEvents",
            "cognito-sync:*"
        ],
        resources: ["*"],
    }));
    const authenticatedRole = new iam.Role(this, 'CognitoDefaultAuthenticatedRole', {
        assumedBy: new iam.FederatedPrincipal('cognito-identity.amazonaws.com', {
            "StringEquals": { "cognito-identity.amazonaws.com:aud": identityPool.ref },
            "ForAnyValue:StringLike": { "cognito-identity.amazonaws.com:amr": "authenticated" },
        }, "sts:AssumeRoleWithWebIdentity"),
    });
    authenticatedRole.addToPolicy(new PolicyStatement({
        effect: Effect.ALLOW,
        actions: [
            "mobileanalytics:PutEvents",
            "cognito-sync:*",
            "cognito-identity:*"
        ],
        resources: ["*"],
    }));
    const defaultPolicy = new cognito.CfnIdentityPoolRoleAttachment(this, 'DefaultValid', {
        identityPoolId: identityPool.ref,
        roles: {
            'unauthenticated': unauthenticatedRole.roleArn,
            'authenticated': authenticatedRole.roleArn
        }
    });

Why is there a UserPool and CfnUserPool? What is difference between them and which one is supposed to be used?

UserPool is a high-level representation of the resource and is the prefered way to work but not all the properties are implemented yet. CfnUserPool (an any Cfn prefixed class) is a low-level representation that maps to a Cloudformation resource. You can use both when the high-level class don't fulfill your necessities, as in the example.

I was able to figure our how to attach UserPool to Identity Pool

    const userPool = new cognito.CfnUserPool(this, 'MyCognitoUserPool')
    const userPoolClient = new cognito.CfnUserPoolClient(this, 'MyCognitoUserPoolClient', {
      generateSecret: false,
      userPoolId: userPool.userPoolId
    });

    const identityPool = new cognito.CfnIdentityPool(this, 'MyCognitoIdentityPool', {
      allowUnauthenticatedIdentities: false,
      cognitoIdentityProviders: [{
        clientId: userPoolClient.userPoolClientId,
        providerName: userPool.userPoolProviderName
      }]
    });

Still struggling with attaching Role to IdentityPool and don't know the difference between CfnUserPool and UserPool. However, this question can marked as partially resolved.