I don't. The only coins I regularly use and hold long term (or think are worth anything, for that matter) are Bitcoin and Monero, both of which support airgapped wallets, offline signing, and transferring unsigned and signed transactions back and forth. I occasionally buy another altcoin for a specific purpose, but since it is always for a specific purpose I am never holding it long term so I just stick it on one of my hardware wallets for the short time I need it.

I have no interest in DeFi, as I think it will go the same way as the ICO craze, the IEO craze, or all the other crazes we see in crypto - a lot of vaporware, a handful of scams thrown in, the vast majority of coins/tokens/projects dropping to zero, meaning some people who gamble on the right project at the right time will make a lot of money, but most people will lose money, and very little of it will survive long term.

There are pros and cons to both methods, and there is nothing stopping you from using both methods. I prefer a permanently airgapped computer with full disk encryption for the bulk of my cold storage. I transfer transactions back and forth using QR codes, using two separate webcams which are unplugged immediately after use, therefore eliminating any concerns regarding transferring malware or malicious code via a USB drive. The computer is stripped of all unnecessary hardware, only runs a basic open source OS and my bitcoin wallet and no other software, does not share peripherals with any other device, is stored in a safe in my house when not in use, and is only used in a room with curtains closed. However, I also use a couple of hardware wallets for funds I want to keep offline, but I will also be transacting with more often than with my main cold storage, which I might only touch once or twice a year. The ease of use of a hardware wallet is significantly higher than that of my main cold storage - just plug it in to my main computer I can be transacting within seconds.

Further, setting up an airgapped and encrypted cold storage device is not a trivial task, especially for someone with little technical knowledge, and there are many places you can go wrong in both the initial set up and the ongoing use. Conversely, buying a hardware wallet achieves a very good level of security (and I'm certain that some would even argue a better level of security), and is far easier to set up and use.

Yes, that is the best. But, while creating the electrum cold wallet, did you created watch-only wallet along? You can use it to track your balance as well. Or, you can check it on blockchain explorer. But, checking it using watch-only wallet is recommended.

Use the link below to be able to create the watch-only wallet:
https://electrum.readthedocs.io/en/latest/coldstorage.html

If you have exported the addresses on a txt file (or the master public key as Charles-Tim mentioned), then you can check their balance. You can either paste your addresses on block explorers and check it via the browser, or import them as a watch-only wallet (on electrum). You can also import them on a Bitcoin client, such as Bitcoin Core. The balance will appear after syncing. Note that the last option is the most preferable if you want to be independent of any block explorers/electrum servers.

On the blockchain.com on generally on the block chain?

A mistake can occur while manually calculating your funds on each addresses. The best is to make use of your master public key (so far it is hierarchical deterministic wallet) to track the whole funds on the wallet with ease. But, why checking for this when the wallet already estimated your balance for you perfectly? You do not need to doubt the estimated funds on your electrum wallet balance.

Since Armory depends on Bitcoin Core, it won't show the balance until it reaches the block where bitcoins were transferred to those addresses.

However as onnz423 says above, if you can export the private (and perhaps public keys) from Armory, then you can import them elsewhere, such as Electrum, and go from there.