1- If we connect the Internet to that machine once or sometimes (to update the Electrum wallet) , will it not remain a cold storage?
Air-gapped wallets means isolation from outer world. Which means it should not have any connection to outer world even there must not be any Bluetooth, or NFC etc. This definition indicates that we should not attach our AG wallet to outside world even if we do it for once or two time then it is not Air-gapped anymore. To update the wallet you could use SD card or usb to insert data into your wallet. In my knowledge most of the wallet even do not have the option of SD card mean to insert data in it. But in current era, new wallets are coming which have many features. like QR scan etc. and more which also lies on security levels.
2- If we are sure that there is no malware or something in the computer, what difference does it make to connect that cold storage computer sometimes to the internet to make transactions?
As per my understanding, we do not connect cold storage to the internet because we fear that any malware may get our electrum seeds etc. Is is right ? There is no other reason. Connecting to Internet, does not mean that the Internet will know the private key or leaks your private key.
A computer can be air-gapped just like a wallet once if it become isolated from outside world. But you are saying you are connecting that computer to online will not make it non-air-gapped. I mean the question is same but you changed the device. i.e. In first question the device was air-gapped wallet and in this question the device is air-gapped computer.
So my answer is same for the Question 1 and 2.
3- If we install electrum on computer (which is malware free and connected to the internet), make a new wallet, keep a note of the seeds and then uninstall electrum from that computer and also remove the wallet files, isn't it secure too?
Secure from what? I mean if you are that sure about your computer being free of virus then what's the need of uninstalling the electrum from it. But still in my knowledge it is not a practical thing to achieve Means not a single computer could remain free of malware. There are numerous types of Malware so new types of malwares will keep coming. But Yeah this method is way secure then keeping that Electrum wallet installed on your device.