Recording & Editing Issues

First, after recording a part, and if I want to record a short part OVER TOP (to fix a few notes), once I press 'record,' the part I already recorded beforehand goes silent.  How do I fix that?
 
Second, when I split a track and delete the part I don't want, it also deletes a previously recorded part under it... it does not delete ONLY the clip on top.  How do I delete only the part I want while not affecting a clip underneath?

Yes... the part I already recorded goes mute.  I still can hear the NEW part and what I'm playing, but it mutes the part already recorded.

OK... I found the problem.  I used to run guitar tracks pro, which did NOT have different record options.  Once I selected 'sound on sound,' both my recording and 'deleting' problems disappeared.  Thank you!