Qs regarding child addresses

In Metamask, I clicked on 'Create account' and it created a new ETH address, but it has no new seed. I learnt that (hope my language is correct) it is a deterministic child wallet created hierarchically from the original ETH address - the seed of which I have backed up long ago.

1. Is it safe from Ethereum and security point of view to use child addresses? Is there something else to know about multiple addresses derived from one which may cause some problem in the future?
2. Suppose I have no transactions on the new wallet and don't do transactions between these 2 wallets. Is it possible for an outsider to link my 2 Eth addresses as being derived from each other? In other words is the derivation of a new wallet given one wallet address possible for anyone to do using a public algorithm or something?

Thanks!