1- If we connect the Internet to that machine once or sometimes (to update the Electrum wallet) , will it not remain a cold storage?
No, it won't. It will be a hot wallet which is sometimes disconnected from the internet.
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?
If you are
sure your computer is 100% impenetrable to attacks and completely free from all malware 100% of the time, then you should probably present your findings to the CIA or something and be paid handsomely in return, since you'll be the first person ever to create a 100% secure system.
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?
No. First, you can't be sure your device is malware free. Second, when you delete data, all you are actually doing is telling your computer it can write over these sectors of your hard disk when it needs to. The data isn't actually removed until it is written over, which could take months or even years depending on how you use that disk.
if we are sure that there are no vulnerabilities in the system, then we can connect to the internet.
You aren't sure. No one is sure. Have you disassembled and intricately examined every piece of hardware in your computer to check for backdoors? Have you read every line of code for every piece of software running your computer, from your BIOS and OS through to your wallet software? Are you examining every incoming and outgoing packet across your internet connect to check for malware or data being leaked? Of course not. Therefore you have no idea if there are vulnerabilities in your system.
This is the
whole point of a permanently airgapped device. It is
impossible to have a completely secure system connected to the internet, but you can mitigate a lot of possible attack vectors simple by airgapping your device
permanently.
Again, assuming the computer never gets stolen, uninstalling the electrum keeps the coin safe even if some malware later comes in that computer and we never re-install the electrum in that computer without formatting it first.
Again, nope. Your wallet data will still exist on your hard drive unless you have deliberately written over the necessary sectors, which few people do. Malware can access that data and send it off to an attacker.