Hi Tarl,
CDCooley has already given a thorough reply to this, but there are a few side-notes I just want to mention.
First off, the follow-distance... in my game it varies quite a lot depending on what she is wearing. If she is travelling unarmored, she's in general pretty close behind me. If she is wearing light armor, she is still not far away. However, heavy armor wears Vilja down, as she has no heavy armor-skill. So, when moving in heavy armor, she is slow and clumsy and can be very far behind me.
So my suggestion is that you dress her as light as possible, as this is something that very much affects her following-distance.
The mod you were refering to is Grab Companion. There you walk side-by-side, but only in 3rd person perspective and there are some other drawbacks as well. for instance, the companion cannot fight while in this mod. However, with Vilja ver 3, you have the option to 'let her lead'. I often just pick a destination close to where I want to go (like if I want to go to Barren Cave I might tell her we're going to Bruma) and then I let her walk independently of me, as I find it much nicer to walk beside her than with her trailing behind. When she is 'leading the way' like this, she will participate in fights etc.
I believe CDCooley's explanation of the combat-options was so extensive that I probably don't have to add anything furhter. I.e. use the "only attack enemies that attack us" but make sure you draw your weapon or raise your fists, cause else she won't fight until your health has dropped a little. Please also read the "Important Information on Gameplay" document (and probably also the Dialog Manual in order to understand all the features) that are inclosed in the zip-file and also available as separate documents. As Vilja of today is different from every other companion, and very different from the ver 1 of herself, reading up a bit will be very useful and help you make the best of your companionship.

Yes, adding some other companions as well might be fun. As you might have seen, Vilja has unique interaction with some of them, for instance the two you mention - Neeshka and Viconia. It will get most obvious when they are in wandermode, but also when they are following and when Vilja is talking to you. Although both companions are nice, the interaction with Viconia is a tad bit limited as Viconia doesn't have so much dialog that works for conversation-interaction (she has an unique voice, whereas Neeshka's voice is the game original elf-voice).