* How do I go about letting my friend know about such a habit of taking and keeping screenshots on his device that I have observed and warn him about it, without looking like I sense bad days coming?
Since you guys had a chat and he told you he wanted to be a bitcoin hodler, then you should be the one to tell him some basic things, like he should avoid taking screenshots of his winnings in the crypto space. You will tell him that crypto scammers are very intelligent and cryptocurrency is not like other stuff he does and shows online. You should tell him things that he would keep secret. He should show everything. However, I believe if he did that, you would have known since the other ones he did, but still, I will say you should advise him.
Although you are not trying to teach him what he is about, whether it is trading or investing, you should just advise him to keep things secret to avoid being scammed.
* My question is, how safe is it to keep screenshots of Bitcoin/crypto transactions and useful information, on ones device?
Even though things are very difficult now, if they are not on our devices, where did you expect us to keep our things that are associated with the internet? For your useful information, there are many ways you can store it in your phone, and you won't get any problems. It just remains for you how you handle your device. If you are giving people your phone, like if many people get access to your device, there is definitely a problem, especially your seed phrase and private key.
These are the most important things you should keep safe in your phone because they are the things that will make someone get access to your funds, so you just have to keep your device safe because they are the things that will make someone get access to your funds, so you just have to keep your device safe and know the kind of people you give your device to.