Every MODX site is unique, so there is no universal place where the footer links are located. It depends on how exactly this site is set up.
Start with the page that you want to make changes to and check the template it uses.
Then open this template in the manager (tab “Elements” → vertical tab “Templates”).
If the information is not directly in the template, then maybe it is included with a chunk. (A tag in the template like [[$footer]] indicates, that a chunk is loaded.)
Simply place a favicon.ico file in your site root. You can also support multiple sizes and device shortcuts by uploading different versions. There’s plenty online generators to help you with all of this e. g. this one.
It looks like you are using two different ways to create a gallery.
In the template “Gallery” you are loading the images from a Template VariablePhotoGallery, that seems to be of the input type MIGX. ([[getImageList? &tvname=`PhotoGallery` &tpl=`galleryItem`]])
In the template “Gallery-Cat” you are using the Gallery extra. ([[!Gallery? &album=`1` &toPlaceholder=`gallery`]])
What lightbox javascript library do you want to use?
For MIGX you probably have to include the JS-library with a <script> tag in the Footer chunk and then add the necessary classes to the chunk galleryItem.
For Gallery there are some built-in options (Gallerific and Slimbox), but they may be outdated.