can you still use an xbox 360 safely

It's a locked down system. It's not like connecting an old Windows XP PC to the internet. You'll be fine.

Xbox 360 console requires unauthorized insides modification to play pirated games from disk. If your Xbox was not open and still under warranty, you can play it safe.

When in the future they decide shut down xbox live for the 360, I suggest before they shut down, download your games to your console just to be safe. You can still play them offline and on system link.

As other have said, there are many people still using Xbox 360s and games are still available digitally for them.

I assume they will still make Xbox One games for at least a couple of years, so you should be safe to buy one now.

I have just bought a One X so hope it will last a few years.

Try the following:

Go to the console settings, and under storage, clear the local Xbox 360 storage.

This will only delete your local copy of the cloud information, so your savegames and profile will still be safe on the cloud.

Then launch a Xbox 360 game, and press the Menu and View buttons to bring up the Xbox 360 guide.

Use the download profile option, and provide your account's email and password to download your Gamertag to the emulated Xbox 360 again.

If you use Two Step Verification, make sure you use an App Password instead of your regular password. You can

create an app password here.