Personal Taxes

The sale of your stamp collection would be a capital asset reportable on IRS Schedule D. It would fall into the category of collectibles and be taxed at a maximum rate of 28%.

The sale of your antique vase would be a sale of a capital asset reportable on IRS Schedule D. It would fall into the category of collectibles and be taxed at a maximum rate of 28%.

The amount of the annual rollover gain to an SSBIC is limited to $50,000 (25,000 if filing MFS).

In addition to the cash proceeds, you should include the unpaid balance of the mortgage as part of the sales price received on IRS Schedule D.

For a residence, the additional costs you incurred are not deductible in the current year. They will be added to your basis for use in the calculation of gain or loss upon disposition. Examples of additional costs are lawyer fees, commissions, survey costs, title insurance, and recording fees. Any mortgage interest and or real estate taxes are deductible in the current year.

If there is an agreement between you and the tenant that the security deposit will be used for the final rent payment, then it is included as rental income in the current year. If this is not the case, then it should not be included as income.

The total amount of your rental losses may be limited in the current year. If they are limited, the limited amount may be carried forward to future years. There are "passive loss" limitations involved with rental properties.
If you have rental income from other rental properties or other passive entities, you may use the rental loss to offset that passive income.
If the rental loss exceeds the passive income, the excess loss of up to $25,000 may be allowed if there is "active participation" associated with the activity and if your Adjusted Gross Income is less than $100,000 ($50,000 for Married Filing Separately).
For Adjusted Gross Income between $100,000 and $150,000 there is a phase out. If the Adjusted Gross Income is more than $150,000, then no part of the $25,000 Special Allowance is allowed in the current year.
Any disallowed loss in the current year may be carried over to future years. In general, "active participation" means you make management decisions. The passive loss limitation calculation is done on IRS Form 8582 and the 8582 worksheets.
Speak to your local CPA about your rental loss deductibility.

Special assessments on such things as sewer systems, local improvements or road repair, are not deductible real estate taxes. These costs would add to the basis of the real estate.

Yes. This is a deductible rental expense on IRS Schedule E.