Self-employment tax essentially is both halves of the social security and Medicare tax. The self-employment tax rate is 15.3%. The rate consists of two parts: 12.4% for social security (old-age, survivors, and disability insurance) and 2.9% for Medicare (hospital insurance). It looks like you had a loss last year, so you would not have paid any self-employment tax, as it is assessed on the net income from self-employment.
It's hard to say why the program is saying that your wife could contribute $7,811 to a SEP IRA, based on such limited information and without the ability to troubleshoot real time. You are correct that a SEP contribution is limited to 25% of qualified income; however, after deducting the potential SEP contribution, it works out to more like 20%. It may be that the program is telling your wife that she can contribute $6,000 to a traditional IRA and another $1,811 to a SEP IRA.
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