1. How should we calculate our capital gain tax. What will be the amount? We bought property for 470K and selling it for 515K. We have not filed for any depreciation deduction in our tax returns till date. We are married and filing jointly.
Actually, *you* don't calculate that when using TurboTax. The program does those calculations for you, based on the data you input to the program. So if you input the correct data, you'll get the correct values. Basically, your taxable gain will be what you sold the property for, minus what you paid for it. You'll also be able to deduct a few other things from the taxable gain, such as your selling costs which includes any realtor commissions you may pay.
2. 11 months back we bought a home for ourselves(let's call it as property B) as our new primary residence. We have a mortgage on this property. Will property B be considered for 1031 exchange for property A?
Understand that a 1031 exchange is not "considered". It's a type of transaction that is planned in advance and per federal law must be handled by a disinterested 3rd party that is properly qualified and/or licensed (if required) to handle that type of transaction. Since it's apparent by your choice of words that you did not do any kind of 1031 exchange, you can basically drop that line of thought. Besides, 1031 exchanges involve "like kind" property. Since you sold a business property (which is basically what rental property is) and purchased a non-business property (property B - new primary residence) the two properties are not like kind. So there's no way this was a 1031 exchange.
3. If we sell both properties A and B and suppose we have capital gain tax on both, then can that money be combined together and applied for 1031 exchange to buy a single property which will be our primary residence? (this may sound crazy but unfortunately, we may have to move again).
The above makes it more apparent that you just don't know what a 1031 exchange is. But that's okay. It's not like you learn this stuff through osmosis. I'm not going to address this question, because by now I'm sure you're well aware that mixing two properties together that are not "like kind" is not permissible with a single 1031 exchange.
4. Is there any way we can save capital gain tax?
Basically, no. Since property A was not your primary residence for at least 2 of the last 5 years you owned it, the sale of Property A does not qualify for the capital gains tax exclusion per IRS Publication 523 at https://www.irs.gov/pub/irs-pdf/p523.pdf since you don't meet the eligibility test which starts at the bottom of page 2 of that document. I'm also fairly certain that you don't qualify for even a partial exclusion since you make no mention of moving from Property A because of a change in workplace location, a health issue, or an unforeseeable event. (page 6 of publication 523)
