Transfering contacts to second 9800

I have a 9800 on its last legs right now and found my father's mint 9800 that he "lost" and got an iPhone instead. I've been reading up on how to transfer all my data from one phone to another, and I'm not worried about that. However, will my old 9800 still have all the original data and be identical to my new 9800? Does this include apps?

My current 9800 has a broken trackpad and is beaten up, but it works otherwise. I also feel that it has gotten a bit laggy, but I don't know what is the cause of that; there is still a lot of phone memory space and memory card space. I have also noticed that my LED indicator will start blinking for a text message, only to get that message a minute later. Sometimes it will also fail to receive group messages and I will have to click "Download now" for it to finally get put into the group message. This happens often in my group chats and is a little annoying. Will switching to my other 9800 fix all these issues?

Back up your old 9800 on DM - name the backup to something you'll remember.
Back up the new 9800.
No need to wipe/erase - depends on which OS6 your device is running.
Restore the new 9800 with your backup - check your restoring correct backup.
You'll need to check on BlackBerry App World to confirm Apps

When it's done, 20-30 mins then your good to go.

Log into your [carrier].blackberry.com and transfer your email address/s to your new device.
Log into BlackBerry App World and confirm device pin change.