Retirement tax questions

All income received up to the date of death at the end of Jan2015 should be reported on the Decedent's final Form 1040.  Indicate deceased and date of death.  So your comment about income is correct with one critical error.  Social Security legally attempts to recapture any Social Security benefits paid in the month of death and any thereafter, usually by a direct debit to the account of deposit.

Since the assets were not transferred to beneficiaries for several months and income accumulated until April, any ordinary income such as interest or dividends and any gain which is realized by the sale of assets must be reported on a Form 1041 for the Estate.  Any gain realized in assets of an Estate, or as inherited by the Beneficiaries, is always considered Long-Term, irrespective of how long actually held.  So you comments there are correct.

The filed Form1041 if final, as all assets were distributed, should be indicated as final at the beginning of the Interview and on the 1041.  All assets were distributed, so you would see that not only is ordinary income reported on the Schedules K-1 but the realized gains and even the realized losses, net amount, will be reflected on the Schedules K-1.  Any other deductible expense such as investment interest, or credits such as Foreign Tax paid, will also transfer to the K-1's.  Again, your comments are correct.

The Estate is not large enough to be liable for Federal Estate Tax unless very sizable Lifetime Gifts were made, which would reduce the exemption.  Depending on state of residency, there may be a state-level Estate Tax.  Estate Tax, if due, is not reported on Form 1041 - please note this.  If it were Federal, it would be on Form 706.  If there is a state Estate Tax, it would be on the relevant state form.  Estate Tax is not part of the Income Tax system.  All assets including received income and all investment assets or personal residence are valued at a "stepped-up" amount - the Fair Market Value on the date of death.