Okay, I think I see what's going on here. Let's take a moment to review how email works and it might clear up how you might want to adjust your settings.
Email is a form of communications between servers. You compose and email and when click "send" the client (outlook, thunderbird, live mail, gmail, yahoo, etc.) sends your message to your host server. The server then looks up the recipient's domain (the stuff after "@" in the email address) and if it finds it, it sends your message there. The receiving server (assuming there is a receiving server on that domain) then looks for the specific account (the stuff before the "@") and if it finds it, saves it to that account. If there is no account that matches, the server will then either move it to a general account and send a message to the sending server that the account was not found, or simply refuse the email, bouncing it back to the sender.
So now let's assume you've sent or received an email and it's sitting out there in an account on a server in a file or database. How you get that email has everything to do with your sync'ing issues.
The most basic email protocol is POP3 (Post Office Protocol) where your email client will contact the server, look for any messages and download them to the client. Once the client responds that the mail was successfully received, it deletes the message from the server, otherwise, the next time you checked, it would download it again.
The other way is using IMAP (Internet Message Access Protocol). This stores your messages on the server so that you may access it from multiple devices and keep them sync'ed.
Let's look at a couple of examples. You have a work email and a personal email. You have a PC at work, a PC at home and a smart phone, and you have both accounts set up on all three devices. This is a common scenario.
You have all your email accounts setup as POP3 accounts. When you check your email at work, all the messages will download to the client. When you get home and check your email, you'll only see email that has been sent after the last time you checked at work. Most mobile phone mail clients are looking at the email header only with POP3 accounts so when you check mail on your phone, any mail on the server will be displayed as the subject and from (and possibly the first line of the body) until you select a specific message. Only then will the message be downloaded to the phone. Most phone clients by default are also set to not delete the messages from the server using POP3 so it will check all available headers every time it syncs.
Now, if you see five messages on your phone, then you check email on your PC and the messages you see on the phone show up on your PC, those messages, once received, will be deleted from the server. The next time your phone syncs, those messages will disappear from the phone.
With IMAP accounts, you use the server to store your messages and the clients simply to view the contents of the messages on the server. In the same scenario as above, when you log into to your email at work home or mobile, you will see all of your email identically. And if you delete the message using any client, it will disappear from all devices.
You want to be able to see all your mail from multiple accounts in one account rather than setting up each account and checking individually, also a common scenario. So you forward messages from A to B. There are a couple of ways to set this up as well.
You can set a permanent forward at the server so any mail that comes in for account A is immediately sent to account B and A never sees it. Or you can set a server copy where any mail coming in to account A is sent to B, but a copy is kept on the server in case you check only account A and want to only see mail for that account.
You can also set the same forwards from your client. The problem with that is that it only works if you check your email from that particular client meaning that you have to make sure you have all your mail settings set the same everywhere or you might not be able to get all of your mail all the time. With a client forward, you download the message from the server, then turn around and send it right back out again. It's just like clicking the forward button only it's done automatically and it's always to the same account. The advantage here is that you can apply filters to the forwards so if you only want mail from one person or domain forwarded, you can do that.
What I think you have going on, is your desktop client (Live mail) is deleting the messages once received so you won't see them on the phone once read on your PC. If you can explain exactly how you want your email to behave, where you want to see it and where you want it stored, we might be able to get you configures so it works as close as possible.
