Taking the plunge

Finally got around to bitcoin after spending all of my 20s bitching about central banks and endless fiat currency wars. Embarrassingly late. Got some dummy questions I’m still not sure about after reading all the wiki’s:

Stating to invest, just on the exchange now, gonna get a cold wallet tomorrow, but still a bit confused on best practices here. It’s best or necessary to run at least partial node on my computer when moving from exchange to the cold wallet?

If I just used paper keys or punched some metal instead, I would basically input the seed phrase into the app of wherever I’m selling?

When I stop using exchanges (literally only used once and won’t again) and move to p2p, what’s the best client? Do I have to be running a partial or full node to do this exchange?

Is it okay to run a node on my laptop I use for everything else or bad idea? Will eventually get a dedicated system and run node full time to help the chain either way.

Do wallets get me to all my BTC with one seed phrase, or is a new phrase generated with every transfer to wallet (does each of my BTC have a different “address” in the blockchain and different keys?).

Thanks yall!