Do wallets save a backup of my private keys and seed? Let's say that I do not trust a lot in myself and my ability to not screw my computer, so also my private keys.

Knowing the concept of wallet HD and having seeds to recover all your private keys linked to the seed, how does this work, from wallets perspective?: 


Does a wallet provider save my private keys (in a secure way) in order to restore them in the future with my seed, if I require it? (Providing paraphrase or information required)
Depends on the wallet provider whether they save a encrypted copy of my private keys to restore them in the future (just in case I remove or lose my local wallet file) or others that they do not save any private data, leaning the entire private keys in my local machine ?


This question is related with some FaQ from.some wallet providers, which they offer the option to restore your private keys providing the seed. This looks like they have a copy of your private keys, otherwise whether you are the only one that have them  and you lose your private keys, there is no way to restore it.
It depends on what wallet you are using.

Most people prefer to use wallets that do not have knowledge of your private key outside of your machine, such as hardware wallets, electrum, Bitcoin Core. This is for safety, since any provider who has your keys could easily decide to move all your coins to an address that only they control, and rob you blind.

That said, there are some services that offer custodial services, usually in conjunction with exchange services. In fact, every exchange is a custodian keyhold for the deposit addresses they assign you on their platform.

A few years ago, perhaps there was some merit in trusting a reputable custodial service who had the infrastructure to always backup keys. In 2018, BIP32/39/44 can make a backup as simple as writing down a handful of words and keeping it very safely, so maintaining control of your keys is the preferred option.