Keep My Email How Does It Work With Outlook

I have two internet service providers, Verizon and another small local DSL/Phone provider.  I have kept the Verizon for several years because neither has very good bandwidth and my household bogs down without 2 mediocre services, and for the email, which I have had for close to 10 years.  Right now the Verizon line is not even usable.  I had to call India twice and actually did get a person to repair the line 2 times.  It worked for three weeks after the line was fixed, now, barely at all.  I'm tired of spending $75.00/month for nothing.  The support is horrible.  The company could care less whether they keep you as a customer.

That being said, I'd like to get rid of it and turn the line over to the other local ISP DSL provider or God Forbid, try Home Fusion,  and keep my email alias which I have used forever.  I don't really want to hear about how I should have a gmail account or this is my fault for not getting an email address not linked to an ISP.  This is what I am working with, and I need to keep the account.

I manage my email locally using Outlook 2010, and I have all of the old email.  I sometimes occassionally use the web-based email, but not often.

First, if I buy the domain before I cancel, will I get my emails addressed to the alias, because none of the parties contacting me have ever addressed anything to the real email name which is a mixture of hard to remember numbers and letters.

Second and in particular reference to Outlook, would I be able to get and send emails from Outlook with the account currently set up for, or do I have to reconfigure Outlook to treat the name preserved under the domain purchase as a new account, and set up a new account in Outlook for the same email name after I purchase the domain to retain the alias email.  In other words can I continue to send and received without any further modification to my existing account as it is now set up in Outlook.

By the way, Verizon has driven me to this.  I would be perfectly happy keeping the DSL if it worked, but I can't continue to support a non-working DSL line to the tune of $75.00 (phone line plus dsl service), with such absolutely horrible support.  I really would like to try the home fusion service but am not yet convinced I should due to all of the reports about the low caps, phantom data usage, and intermittent service from some.