Popular overnight

If I'm about to start exchanging some links, does it matter if it's done over a short period of time like overnight or a longer period of time say in a couple of months? Does a large SE consider it more natural if it's done over a longer period of time?

Yes. Google will notice if you're going to have a large number of incoming links in a short period of time and might add some penalty for links. Talking about exchanging links it will be even worth.

Regarding exchanged link (pages linked to and from) I understood that google made same changes in the algorithm so those links are ignored. Can someone confirm or infirm it?

Good question: you can start a new topic for that!

There is nothing ignored. They might be devalued , but still in the game.

It is widely accepted that getting links slowly over the time is better than getting them all overnight. It might not hurt you but it will not be of much help either.

Question: Can it be called "Link Juice"?

link juice i think is weight that is divided amongst your site links. so if you have a ton of links to external domains, each link will get less 'juice'. i believe this is also true for the internal links to your own site meaning you would be devaluing your own links by having massive amounts of 3rd party links.

whenever you exchange links however, be sure to monitor the traffic, if any you are getting from the particular site. be sure they havent placed a rel=nofollow tag in with your link if your giving them some of your juice!