How to access Outlook.com without giving them the phone number or another email address

I have verified mine with just a credit card by following the "Add a credit card" option - just gone in and checked it now. The process involves PayPal charging a nominal small fee to the card, then you enter the code that will appear on your statement.

They still would prefer me to add a bank account to the details page (they offer to lift receiving limits if I do this) but my account is verified purely from the credit card validation.

(Caveat - I am in the UK. Rules may be different)

Does Hotmail or Outlook.com have a similar feature?

Yes, Outlook.com has that feature as of this week.

If yes, how does it work?

This blog article explains how it works. It works the same as with Gmail.

Example

Say your email address is myname@outlook.com. You can add something with a plus + sign. So, sending an email to myname+mailinglist_topic_x@outlook.com will still be delivered to myname@outlook.com.

Then you can create a rule with, for example, the filter To-line contains myname+mailinglist_topic_x@outlook.com and redirect those emails to another folder.

_{Image source: http://www.ghacks.net/2013/09/17/can-now-use-email-aliases-outlook-com}