The amounts shown in boxes 1 through 20 reflect your share of income, loss, deductions, credits, etc., from partnership business or rental activities without reference to limitations on losses or adjustments that may be required of you. A discussion of these limitations is available in the instructions available at http://www.irs.gov/instructions/i1065sk1/ch01.html#d0e159
Ordinary income is usually reported on Schedule E Part II line 28. However, your interest in the partnership is likely a passive activity so you would also use Form 8582 to determine if any of the passive loss is allowed.
Line 13 placement on your individual return will depend on the code in that box. See http://www.irs.gov/instructions/i1065sk1/ch02.html#d0e1180 For example, Code G investment interest expense is entered on Form 4952, line 1.
Line 14 only applies if you are a general partner in the partnership.
Line 20 placement on your individual return will depend on the code in that box. For example, Code A investment income is reported on line 4a of Form 4952. See http://www.irs.gov/instructions/i1065sk1/ch02.html#d0e1738
You are correct that if there is no entry on line 17 then there is no additional entry needed for Form 6251.
I hope this helps for reporting your Schedule K-1 from the oil and gas partnership.
1) Passive loss rules do not apply; but at-risk and basis limitations may (or may not be applicable)
2) Use Schedule SE to report the amount in line 14.
3) Code I. Section 59(e)(2) expenditures. On an attached statement, the partnership will show the type and the amount of qualified expenditures for which you may make a section 59(e) election. The statement will also identify the property for which the expenditures were paid or incurred. If there is more than one type of expenditure, the amount of each type will also be listed. See the line by line instructions at http://www.irs.gov/instructions/i1065sk1/ch02.html#d0e1180
Make the election on Form 4562. If you make the election, report the current year amortization of section 59(e) expenditures from Part VI of Form 4562 on line 28 of Schedule E (Form 1040). If you do not make the election, report the section 59(e)(2) expenditures on line 28 of Schedule E (Form 1040) and figure the resulting adjustment or tax preference item (see Form 6251, Alternative Minimum Tax-Individuals). Whether you deduct the expenditures or elect to amortize them, report the amount on a separate line in column (h) of line 28 if you materially participated in the partnership activity.
4) Code A. Net earnings (loss) from self-employment. If you are a general partner, reduce this amount before entering it on Schedule SE (Form 1040) by any section 179 expense deduction claimed, unreimbursed partnership expenses claimed, and depletion claimed on oil and gas properties. Do not reduce net earnings from self-employment by any separately stated deduction for health insurance expenses.
5) Code T. Information needed to figure depletion-oil and gas. This is your share of gross income from the property, share of production for the tax year, etc., needed to figure your depletion deduction for oil and gas wells. The partnership should also allocate to you a share of the adjusted basis of each partnership oil or gas property. See Pub. 535 for how to figure your depletion deduction
All of these items are explained at http://www.irs.gov/instructions/i1065sk1/
I hope this is the information that you need.