RE:   Sorry, I do not understand the differences between Ln#39 - Reg1.861-10(e) and Ln#40 - Reg1.861-10(T).  Does anyone have idea which Reg does mortgage interest expenses belong to?

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Line 40.

First, is your interest deduction subject to Reg. 1.861-9T, Allocation and apportionment of interest expense?  Bear in mind Section 861 deals with "Income from Sources within U.S." 

If YES, does it fall under the three exceptions under Reg 1.861-10T?

(a) In general. This section applies to all taxpayers and provides three exceptions to the rules of § 1.861-9T
(b) Qualified nonrecourse indebtedness -
(c) Direct allocations in the case of certain integrated financial transactions -
(d) Special rules. In applying paragraphs (b) and (c) of this section, the following special rules shall apply.

Thus, if your reporting is subject to 1.861-9T AND also one of the three exceptions applied, report on

Line 39.

If your reporting is specifically subject to the allocation rule under 1.861-10(e), report on LINE 39

What is 1.861-10(e)??  Here it is:

§ 1.861-10 Special allocations of interest expense.
Link to an amendment published at 87 FR 326, Jan. 4, 2022.
(a)-(d) [Reserved]

(e) Treatment of certain related group indebtedness -

(1) In general. If, for any taxable year beginning after December 31, 1991, a U.S. shareholder (as defined in paragraph (e)(5)(i) of this section) has both -

(i) Excess related group indebtedness (as determined under Step One in paragraph (e)(2) of this section) and

(ii) Excess U.S. shareholder indebtedness (as determined under Step Two in paragraph (e)(3) of this section),

the U.S. shareholder shall allocate.....

The (i) and (ii) above are specifically defined thingies that, if you're subject to Sec 1.861 in general, you should read the detailed definitions.  (zzzzzzzz)

Others - Line 34

If you're NOT eligible for the 1.861-10T exception, and NOT subject to 1.861-10(e), and you're subject to the 1.861 allocation, Line 34.

If you're NOT subject to Reg 1.861-1 et al., and NOT required to file K-2/K-2, why would you care?

Here's from the Form 1065 Schedule K-2/K-3 filing instructions.  Emphasis added:

Who Must File

The partnership need not complete this schedule if the partnership does not have items of international tax relevance (typically, international activities or foreign partners). Any partnership required to file Form 1065 and that has items relevant to the determination of the U.S. tax or certain withholding tax or reporting obligations of its partners under the international provisions of the Internal Revenue Code must complete the relevant parts of Schedules K-2 and K-3. See each part and section for a more detailed description of who must file each part and section. Penalties may apply for filing Form 1065 without all required information or for furnishing Schedules K-3 to partners without all required information. The penalties that apply with respect to Form 1065 and Schedule K-1 apply with respect to Schedules K-2 and K-3, respectively. See Penalties in the Instructions for Form 1065.

Note. Except as otherwise required by statute, regulations, or other IRS guidance, a partnership is not required to obtain information from its direct or indirect partners to determine if it needs to
file each of these parts.

Note. A partnership is only required to complete the relevant portions of Schedules K-2 and K-3, as applicable. For example, if the partnership does not own (within the meaning of section 958) stock of a foreign corporation other than solely by reason of applying section 318(a)(3) (providing for downward attribution) as provided in section 958(b), it is not required to complete Schedules K-2 and K-3, Parts V, VI, VII, and VIII.