You visited the departments because it was an internal interview process. This is totally different.
Unless you're still in contact with her anyway it would look weird and potentially inappropriate to contact her to say you're applying. I would expect most people to interpret that as an attempt to milk them or gain an advantage.
I honestly have never heard of anybody even think about asking to visit a company in advance of an interview to look around. Unless it was a retail business where you could visit a shop or something. You suss out the company at interview - they give you space to ask questions. Businesses don't have the time or spare resources to arrange tours for random third parties wanting to apply for jobs - can you imagine how many people that might be? Plus all the security issues involved in that.
If you get the interview, entering the building ten minutes early gives you time to get a bit of a feel for what it's like, how people are, the environment and surface culture etc as well as calm yourself a bit. Any earlier and it's awkward, later and you don't have time to absorb things. And obviously be aware that the receptionist will probably be asked for their impressions of you after you leave.
As for research, the own company's website yes, but also the sector and competitors. Gain an understanding of how they position themselves in their sector and against competitors, what's different about them, what their strengths are, what they're known for, what the challenges are for the business, where they're aiming over the next few years, what you can glean of their culture, how they're regarded by others, etc.
Knowing what they say about themselves on the website is important, but you need to know more. And it's less impressive if you sound like you're reciting their website back to them!
You want to know the things that are important to them so that you can highlight how that fits you and your experience, and so you can pitch yourself and your communication skills in a style that fits theirs. Speaking their language basically.
Networking is about building relationships and maintaining them (and in the context of an existing maintained relationship mentioning you're thinking of applying would be normal and unproblematic), so that's a worthwhile endeavour as a separate exercise. Networking is not contacting somebody out of the blue to tell them you've applied to work at their company.