I was going to suggest Tether... as an alternative to TrueUSD, but I note that Tether is now also an ERC-20 token.
So, in essence, all you would need to "store" your TUSD/USDT is to create an ETH address (using MEW or MyCrypto wallet etc)... and then send your TUSD/USDT tokens to that ETH address, then export your private key.
The trick then is to figure out how to convert your BTC to TrueUSD (or Tether)... and then back again.
Will I have problems when exchanging from TUSD to BTC? What is the best solution to get any stablecoin "with the private key" without verifying identity or using any platform?
I'm not sure what you mean exactly by "without using any platform"? You mean you want to convert without using a centralised exchange that might require KYC? If so, the only way to achieve that would be via a DEX (like IDEX or Waves or EtherDelta etC)... or P2P trading (Escrow recommended etc).