1. You can check how display:none is supported across email clients on Can I email. (Disclaimer: I’m the maintainer of the site.)

2. HTML and plain text are two separate versions of an email. It’s up to you to send both versions and make sure that the content is relevant. From what I see from a WooCommerce I have, with the Storefront theme, it is set up by default to only send a text/html. You can change this WooCommerce > Settings > Emails, select an email and change the “Email type” value to Multi-part. You can then see in your admin the file you need to edit for the plain text version in your theme.

3. You can use screenshots testing tools like Litmus (the biggest, well-known tool in the community), Email on Acid (my personal favorite) or Testi.at (good to have if you have a low budget).

1. The display: none property is fully functional at least on Gmail since 2016, but not in Outlook.

2. If the email do not recognize the property it will be just ignored. (In this case the inside will be shown).

3. So if you want to create e-mails and make sure that is working I believe the best way to be sure that is everything OK is to test, create email accounts in various services, and send emails to yourself.
   Most minor email services will follow the same rules as the bigger ones.
   There some tools that can help you test it, you can see it in this quetion.

More tips for creating emails with HTML here and here.

Display none works on almost all email clients. Outlooks are notorious as you might have seen. Below is a piece of code we use to hide preheaders.

<div style="display:none;font-size:1px;color:#000000;line-height:1px;max-height:0px;max-width:0px;opacity:0;overflow:hidden;mso-hide:all;">
<!-- pre header -->
 </div>

There are different variations of this online but what you are after is display:none and mso-hide:all. mso-hide all is specifically for Outlook and will hide any element it is on. Just remember, if you have nested tables, it will need to go on all of them.

I’m currently customising my first (woocommerce) email template and I’d like to hide data via CSS display: none

However, I’m wondering what the support of CSS and display: none is, i.e.

1. do all email clients support basic CSS such as display: none or is it too much?
2. what happens if a receiver views emails only in text format (not HTML)? Does the email client convert the HTML to text (i.e. the display: none is still not shown) or does the the email client just put out the plain text it can find without HTML conversion (i.e. display: none content is still shown)?
3. is there a website to test how emails will look across email clients (outlook, gmail, yahoo, spark, mac etc)?

I know this may be very basic, but I’d truly appreciate any help !

Many thanks

Update:

This website provides some details on hiding elements: http://www.emaildesignreview.com/email-code/hiding-elements-in-email-4922/

I’m currently using the following to try hiding on as many clients as possible:

font-size: 0; /* in case display-none isnt working */
max-height:0px; overflow:hidden; /* for gmail */
opacity: 0;
visibility: hidden;
display: none; 
mso-hide: all; /* for outlook */