You asked:
And another question following on from this is: does your brain easily switch between styles in a similar way that a multilingual can switch between languages, once you have perfected a new style of handwriting?
There is no 100% rule on this topic. Just as some people have a real knack for languages, some people have a knack for learning many different styles. Most people have trouble switching, but it is a very personal matter. I've seen people who can switch at will, but that is not typical. For me, if I need to brush up on a style I have not done in a while, it only takes about 20 minutes until I am happy with the results. If I have a whole day to practice, it will be even better.
Switching back and forth between styles during a 2 hour practice session is not going to be very helpful. But working on your italic one day and your copperplate the next day is fine - for some people. There is a lot of carry-over between styles. Learning to look at your white space and developing rhythm are two things that you need to work on - and it doesn't matter what style. You have to figure out what kind of learner you are. Some people are better learners when they can jump around a bit. It's not the way I learn, but as a teacher, I found out that it was better to let people find their own groove. I started with broad edge and it was my comfort zone for quite some time. Pointed pen styles didn't feel right. Then, Mike Sull recommended Nikko G, McCaffrey's ink and Clairfontaine paper and it changed everything. Suddenly pointed nib scripts were my favorite.
IMHO, the key is finding that tactile sensation that makes you lose track of time - so that the practice is mesmerizing. Allow yourself to try as many different styles as you like until you find the one that feels the best. Seeking out the best nib-ink-paper combination is also a key component to the process. Don't forget to try the humble pencil when you do not have time to get out the nibs and ink.