How can I connect these pipes...?

In both instances you can use pushfit tap connectors. There is a female threaded connector for the tap tail or toilet inlet, and a pushfit end for the copper pipe connection. Pushfits are reliable, reusable and easy to use. All DIY stores will have them. Be gentle with the connection to the toilet inlet (don't cross thread it) as they can strip threads if you are heavy handed. Just tight enough to stop leaks.