No, storing them online is definitely not recommended. Instead, you can create a paper wallet (make sure to encrypt the private key), print it, and then hide it.

Here is a recommendation for you using washers, it's how to secure your seed phrase https://bt.irlbtc.com/view/5389446.0 try go through the thread and get some important tips that could help you secure your keys safely, but i will add it as an additional caution for you not to use the centralized storage networks in handling them for you, your wallet keys must be far away from the reach of any third party be it in person, organization or online storage.

I suggest you stop listening to their advice in the future. Even if you are not trying to store your private key/seed phrase, using online storage to store sensitive data is never a good idea. Have you never heard of how many people lose their account/money because they save their password on their Evernote, Google Keep, e-mail, etc?

Personally, I store my seed phrase offline with encryption that only I know of, in a very secure location, and regularly check them out to see if anything is broken. Definitely not the best way but it is good enough for now, and I'll try to improve it in the future. I can't really protect myself from memory loss, so what I can do about that is just try to live as healthily as possible. Relying on our memory to remember the seed phrase is not a good idea anyway, just make sure to remember that you have some crypto and seed stored somewhere. CMIIW.

You should search around this board to find out how to protect your private key better. There are tons of threads talking about it other than what has been mentioned above.

Do not try to remember your private key you are going to forget it eventually. I recommend writing your private key and seed on paper and storing that safely. Do not make a copy of them on a digital device because digital devices can fail and you might lose the back up. If your device is connected to the internet then it can be stolen. Only physical back ups and do make sure they are stored in a safe location.

Protect against natural disasters as well as thieves. If you need to access your btc regularly I recommend using a hardware wallet because they stop certain hacks and keep your btc safer then a normal btc wallet connected to the internet.

There are two ways for you that you can adopt. Passwords are very secretive which if disclosed can lead to loss of valuables including assets.

1. First you can write down the secret password on a piece of paper.  It can be diary, notebook etc. Keep it written down on paper near you. The outsider should not find it.
2. If so, you can remember short passwords yourself. Remember passwords that are never hacked and are the most secure that you have written down.

If it's possible to avoid using any app that uses internet connection and since Gmail uses the internet then it's not advisable to use it and that friend of your that gave you that idea probably hasn't seen anyone that has been hacked before or maybe they're just trying to play dumb by avoid all red flag and still continue using it to save their private key.
It's better to save it offline and one of the way of doing that is by using a nail or any sharp objects capable of scratching a steel plate, write your secret phrase or private key on the steel plate and then keep it in a place where you know that no one will ever think of looking at. By using steel plate you have successfully avoided the risk of your private key getting destroyed by fluid and also getting erased easily unlike those written on a piece of paper which are prone to water and been erased.

I suggest never store your private key online as it can be hacked including in Gmail and others online, and if your private key is lost or hacked then you will never get it back and your ownership will be lost.
you should save your private key using paper that is very safe from anything and put it under your bed or anywhere and make sure only you can find it, it's better not to ask friends for advice to save your private key. Because there is a possibility that your own friends will steal or hack, especially if your friends know the nominal, and prevention is better than cure.

You don't remember what? Fifty base58 characters, case sensitive? Are you mad? You should never memorize private keys. Hell, you shouldn't even look at them, there's no benefit and it adds a little risk to mess it up.

No clouds, no mails, no private keys. Just generate a seed phrase on an airgapped device. Let me quote myself:

Good thing you are asking now before you actually misplaced them or loss them and begin to seek remedy.

This means you should be careful with who you ask for advice and whose advice you take because everyone always has something to say  and it does not always mean that they are right.

When you are asking for advice, always ensure that you ask people who you are sure and qualified to answer you correctly and not just random people.

While considering private key safety many suggestions have already been mentioned in posts, but still private keys are the ultimate source to access crypto electronically, without a private key no one can get access to crypto assets. So keeping them safe and secure is the most important task.

As Gmail, any drive, or any cloud services are third-party and completely centralized services that may keep watch on data stored electronically, so never keep any confidential data on electronic platforms. It may bring trouble.

The second important task to keep your wallet safe is never to use your wallet for suspicious sites by allowing to access them.

Many phishing sites have extra scripts embedded within websites that get access to the wallet and may harm your equity.