Q. Can I receive any tax deduction for this furniture or consider it a part of the cost of this new apartment?
A. There is no deduction for that. Also you cannot add the cost of the furniture to your cost basis.
Q. Would I be able to count this cost to cover the earnings from the sold apartment?
A. No.
The old tax law (more than 20 years ago) allowed you to avoid tax on the sale of your home, if you invested the money in a new home. That is no longer the case. It does not matter what you do with the money, the gain on the sale is taxable, unless you qualify for the home sale exclusion.
As you apparently know, to qualify for the home sale exclusion, you must have lived in the old home 2 out of the last 5 years.
However there is an exception to the 2 year rule for "unforeseen circumstances". You may qualify, for a reduced maximum (less than $250K) exclusion. See:
http://www.journalofaccountancy.com/Issues/2009/Nov/20091783.htm
