What do you use to read and write emails?
Thunderbird. It sucks, but it sucks considerably less than Outlook (which may take 20 minutes to start up at times, doing some database checks or whatever it does, and which consumes a major part of your computer's resources) or any other mail program that I've seen.
I try to avoid email when I can, as I find it to be a rather antiquated medium.
Well no, just the protocol is antiquated (like pretty much all protocols on the internet) and the people writing the clients aren't putting a lot of effort into it either (or so it seems, there is no single good email program that I know of, nor a single one that interoperates with any other program in a seamless way).
Nor is there any effort in trying to improve it because that obviously contradicts interests of both major companies and governments. Government wants to read your mail, and so does Google (and others).
There is no working encryption, which should actually be standard (please don't mention PGP and such, stay real). There will never be either.
Instead, government-certified companies are starting to sell fuckshit like De-mail (that started this year in Germany) which makes a big deal about using TLS-secured connections to the server and the "trustworthy" company sending out legally binding return receipts in your name. But of course there is no end-to-end encryption, and the same "trusted" companies forward your mail directly to the NSA.
In other words, you are to pay €€€ for getting no benefit over regular email and the quite possible inconvenience of Telekom or United Internet alleging in a legally binding way that you've received a particular email although you haven't. Which, seeing how incompetent they are at other basic things (like, keeping a deadline, or fulfilling an order), is quite possible.
Still, email - as it is - is very useful. You can't tell your electric supplier or your insurance company on Twitter or Facebook that you want this-and-that. Email does that just fine. The general idea is good. In practice, it could be much better, but it only isn't out of choice.
Do you check for emails every now and then or do you keep a client open for instant notification?
Both. It depends.
Do you care about google reading your emails (even business ones) when you use gmail?
Gmail != business. Other than that I don't care about Google reading my emails since the US spy agency pigs read them anyway.