A wallet isn't supposed to ask you to verify your identity, an exchange is. You could just use Blockchain.com or Guarda if you're in need of a web wallet, but I wouldn't recommend it . I'd go with a desktop wallet like Electrum or for your smartphone, Mycelium.
There is no Hardware wallet called Treasure you might be talking about Trezor wallet?
For online wallet, it's already mentioned above but I do not recommend you to use Blockchain.com wallet because it's a buggy web wallet and for Android, you can use Mycelium as mentioned above but Electrum also has an Android version so try that first.
Other mobile wallets can be found here
https://bitcoin.org/en/choose-your-wallet?step=5&platform=androidFor a web wallet that you can run offline use this
https://coinb.in/#wallet In the future I will buy a hardware wallet like Treasure but for now I am looking for temporary free wallet. Thank you.
Treasure?
Never heard of. I strongly recommend that you use Trezor or Ledger Nano hardware wallets. Those hardware wallets are in the market for long time and are very reliable.
I do not recommend using web wallets, but if for some reason, you have no other alternatives and this is your only option, at least make sure it's a non-custodial one. Meaning it gives you access to your wallet seed/private keys. This way you will have full control over your wallet and you can recover it any time you want.
Blockchain.com is a non-custodial wallet and does not ask for kyc. They also have an open source app if you want to use it on your mobile.
Yes I meant Trezor the automatic translation missed. Thank you for youe help. The thing is that in the meantime I unfortunately do not have enough money so I thought to use for free wallets at the moment. Mostly mobile wallets will be better for me. I understand that most of you recommend Mycelium and Blockchain. Does anyone have any more opinions please