I know that a Druid can release an animal companion from service and get another one (or replace a dead one) for 24 hours of interrupted ritual. Is it the same for Ranger?
Yes, everything is the same except that the ranger is treated as a lower-level druid.
How does summoning happen exactly? Do the animals just pop into existence like a Summon Monster spell or does the Druid or the Ranger try to call an animal into their service with their rituals? Can they call any kind of animal regardless of the biome they are in?
This is… ill-defined. The rules state only that a 24-hour ceremony provides a new animal companion, selected from the list. Other supplements (most notably the It’s Hot/Cold/Wet/Crowded/Not Outside series) provide alternate lists for druids in particular environments, and most campaign settings also tweak the lists by region or whatever, which implies that the animal you get is dependent on where you are… or maybe on where you’re from. It’s not really stated one way or another.
Ultimately, it’s up to the DM. I have tended to play it that the druid must find the animal first, and then perform the 24-hour ceremony to bond it, but it could just as easily be a 24-hour ceremony beseeching nature for the companion of choice, which is called to the druid regardless of local availability. (this would not be like summon nature’s ally, as those are very temporary, but a Conjuration (Calling) effect, like a druid’s version of planar ally or planar binding)
It could be that a druid is specifically empowered by the natural environment in which he was trained, or where he grew up, or where he currently finds himself, and so the answer to the call is performed by whichever of those is true and thus the animals available are limited by those environments, or it could be that all of nature at once empowers him and supports him, and any animal is available.
It could be that the ceremony requires deep knowledge of the animal in question, knowledge only gained through first-hand experience, or it could be that the druid merely describes the features he’s looking for and nature provides just the thing.
Any of these are possible interpretation of the rules, and have more to do with the setting of the game than they do with the druid himself. These are cases where Wizards has not only allowed you, as DM, to make a call, but required you to do so.
For balance’s sake, I recommend putting some kind of limitation on it. The druid is fantastically powerful, and while the animal companion is the least of the trifecta (spellcasting, wild shape, animal companion), it’s still really potent. So discuss this with your players and consider the setting you’re playing in, and come to a decision.
When an animal companion dies, do they disappear like how a creature summoned by a Summon Monster would die, or do they die like a normal animal?
They die, like a normal animal or like a creature called with Conjuration (Calling). They definitely aren’t summoned, and therefore do not simply disappear. I cannot prove a negative, but nothing references the Conjuration (Summoning) rules and animal companions are never stated to be affected by anti-summoning spells like magic circle against evil.