No, your husband's non-PA income does not need to be filed with Pennsylvania. You are allowed, and virtually required, to file a separate return for the time that you lived in PA. This except comes from the PA tax instruction manual, chapter 4, page 21:
Married taxpayers must file separate returns if-
• One spouse is a resident and the other a nonresident, unless both spouses elect to be taxed as resident taxpayers; or
• The taxpayer's spouse died on or before the last day of the tax year (surviving spouse files as "single" unless he or she remarries before the end of the taxable year). A return must be filed for the deceased as “Deceased";or
• If one spouse’s taxable year begins or ends on a different date; or
• If either spouse is liable for the payment of spousal and dependent support; or
• The taxpayer or spouse claims any restricted credit listed on PA Schedule OC, Other Credits, such as the: Employment Incentive Payments Tax Credit; Jobs Creation Tax Credit; Research and Development Tax Credit; Film Production
This really answers all three of your questions. For 1 and 2, the answer is no, it is not reportable to PA if you file Married Filing Separate in Pennsylvania (which is allowed even though you file a joint Federal Return). And, yes, it will be reported to and taxed in Kansas.
But because you should file a PA part-year return as Married Filing Separately, you will want to see this FAQ on how to do this: https://ttlc.intuit.com/replies/3302008
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