Yes, you would pay tax on the $6,000 in your traditional IRA when converted to a Roth IRA. Since all of the original contributions were deducted, then all of the money would be taxed upon transfer to the Roth. This would not be considered as a capital gain, rather a distribution from a retirement account. Capital gains will not apply in this situation.
For the question on nondeductible contributions to a Thrift Savings Plan (TSP) - this is a tax and retirement savings plan which allows for deductible contributions only. This plan is specifically set up for deferred tax treatment. This means when the money is distributed it will be taxed.
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