Restoring to Mountain Lion.

Hey guys!
I am using mac from the past one year but sadly, I am still a mac newbie So, I need your help.
I had Sleopard when I got my early 11 MBP and upgraded to Lion with the free up to date program. Since then my mac has been acting like an old Windows pc with impotent hardware, hanging every now and then, freezing, super slow.
So, Mountain Lion was a blessing! I did a clean install of it on my Startup drive using guides available.
I had prior to installing Mlion, made a new partion of my HDD (320GB) and used that to take a time machine backup of my drive. The backup is there, and I can access those files even now using finder.

Now, I want to restore my files (images, music etc) as well as some apps but nothing that will cause the old problems to come back. I can use Migration Assistant to restore the user files easily I know, but user account names are different so will it work fine and restore everything to its proper place?

Also, if I start time machine ie enable it, and select the same partition where my old backup is (of the lion install) what exactly will happen? will it overwrite that? create new folder or what..

How do I restore specific apps? I can copy paste from Finder, but is that the right way?

Those are few questions I'd be glad if I get some advice on. Basically it comes to restoring data from an old install in such a way which does not bring old problems back.

Thanks!!

Edit: I have another query.
I had this problem in Lion too, thought it would be fixed if I cleaned install (was lazy to do so), now cleaned install MLion after a year, still the same problem.
If I leave my laptop to sleep mode, then when I wake it up again, it will never connect to my wifi network!
A) I HAVE TO HAVE reboot my router
B) I HAVE to restart my macbook pro.
to fix this and to make it able to connect to my hotspot again. nothing else seems to fix it.