Jim - the gallery plug-in I used is open-source.
Joomlaworks Simple Image Gallery
As far as getting things in the right place on the right page... for me it all depends upon the template I'm using and the location of the "positions".
Gary - the slideshow you have is also by Joomlaworks and it had to be purchased. I don't have any experience with that one... but from looking at their site I don't believe the gallery "mambot" that I'm using was included.
As far as getting rid of the "new images" title showing up... I'm not good enough to figure it out by looking at the source code so I'll have to ask a question...
- is the homepage set to show to a static content item or a component?
You can find out in the admin area by going to the "Menu Tab" and selecting mainmenue (assuming you haven't changed this) and then looking at the first published item. Underneath "type" what does it say?
Sorry for not being able to provide immediate answers, but feel free to ask whatever questions you need... I'll be first to say when you've reached my knowledge limit.