I bought my apartment for $115000 and after 10years living in it I sold it for $136000,do I have paid the IRS tax?

You paid $115,000 and received $136,000 on sale, realizing a gain of $21,000. You should also have closing expenses, plus significant updates/remodels, right? All of that can get rolled into your "basis" in the apartment, which would reduce your gain realized.

Whether you will have to pay tax on this amount depends on whether you meet the requirements to exclude gain on sale of your primary residence. If you have owned and lived in that apartment for 2 of the last 5 years as your primary residence, you did not acquire the apartment in a 1031 exchange within the last 5 years, and you have not claimed a primary residence exclusion within the last two years, you will most likely be able to exclude the gain (up to $250,000, which isn't a problem here) from your taxable income and not pay tax on the amount.

HOWEVER, because these sales are reported to the IRS, you will need to include these amounts on your tax return and affirmatively claim the primary residence exclusion on the return.

If you have any questions about any of this information, I suggest you consult with a duly licensed tax professional (EA or CPA) for assistance.

No.

As you have lived in it and owned it for at least the past 2 years, the first $250,000 ($500,000 if married) in profit is completely tax free.

The "reinvest in another property" rule went away in 1997.

If you properly report the sale, including showing how much you paid, how much the profit was, how long you owned it, etc., then no, you don't pay.

However, if you don't report it, then you pay tax on the $136,000 (you don't get credit for the $115,000 if you don't report it), plus you also pay the penalty for not reporting it.

How long did you own it? If over 2 years, no.

you will have to pay tax on your profit. I think you can avoid it if it goes into your next house. So if you keep climbing into better houses you wouldn't have to pay anything.

Nope.

if you are single you are entitled to the $250000 exclusion