Getting on the first of the three posed questions - so far, most of the comment has been on the second one - I'd say it's okay for a country to pose some minimum requirements for citizenship, not just the applicant having lived in the country for five years or whatever it is. Being able to read and speak the main language/s (at least one of them, if there is more than one official language) with at least some fluency is a legit demand for adults - you can get nowhere today if you don't know the language of the place you live in, and, seeing this as a non-U.S. person, knowing English but nothing of the local tongue isn't quite enough. Most adult people in my neck of the woods have picked up some fluency in English, from basic to practically bilingual, it's been that way for decades, but on the job, taking the train or in stores you'd still be pretty much considered a cypher if you're a local, steady resident, clearly not an immigrant who arrived one or two years ago, but insisting on always speaking English, and not responding to any replies in Swedish, the national language. This shouldn't be controversial (at present there is no such rule or law where I live; there is next door in Denmark though): in the U.S. one also has to show some knowledge of English, among other things, to become a citizen. Some minimum bar of understanding of the principles of democracy, free media and of a secular justice system would be fine too.
Certain serious crimes committed during the time the applicant has lived in the adopted country, or very serious crimes that surface from their past, should constitute a bar against citizenship as well. No country wants to become a haven for murderers, war criminals, major druglords or illegal weapon merchants. Or convicted, hardcore terrorists - I mean people who have directly taken part in terrorist acts or personally supported such acts with money, sheltering active terrorists, setting up transports for them, faking passports or the like, that's something I suspect most Americans here on the forum would agree with.
When it comes to ID controls leading up to citizenship, the data that end up in the records and on the new guy's passport, if it's let's say a refugee from Africa or the Middle East, or someone who has adopted a new identity somewhere along the way and acquired papers for that id - those data are ultimately the ones offered by the applicant. Europe accepts far more refugees and asylum seekers than the US - both because we're more exposed, closer to the trouble spots, and because policies of immigration, intake of refugees and asylum seekers etc are different - but the problems with ID data, at root, are the same. If an extended family of a dozen arrives in a trailer, having travelled 2.500 miles over a timespan of a year, with stops on the way, and they say they are so-and-so from Pakistan or Libya, fleeing from oppression, gangster rule with no police presence or simply intolerable living conditions, and the seven juniors all say (in Arabic, interpreted to the local language) that they are the children of the central couple of the family, how can we know they are who they say they are? Some of the kids might be some neighbours' kids, some of the names and places of birth may be fake.
Immigrants often burn their passports or they're confiscated from them by the people who smuggle them along, so the people at the border crossing might be in no position to determine with certainty who these people are. Showing up without a passport or any really trustworthy documents is a way to pose a fait accompli to the border guards, and it works in countries that don't have a hardline policy of refusing entry outright to everyone seeking asylum unless they can prove who they are and prove they have actually been persecuted (some will be rendered out of the country anyway according to policy in many countries here, but then only after an inquiry into whether they should be allowed to stay).
Obviously you can get in on a fake identity, and ultimately become a citizen on such an identity, getting a legal passport. What if it turns out, after you've become a citizen, that the original story was a fake? It used not to be a big overall issue - illegal migration was limited during the cold war: it was plainly hard to get from southern Asia or Africa to Western Europe unless you had resources and decent papers. Controls, checkpoints and especially the iron curtain stood in the way (many people these days travel through Turkey or Russia). Also, some states had laws that provided for repeal of citizenship if the data given had been faked or if someone had committed really serious crimes after settling in their new country. Now those kinds of laws are rarer, they're seen as troublesome. I personally think a country should have the option to withdraw citizenship if it's proven that the original data were fake (and the real identity seems to be something more disturbing) or if the applicant has committed some specified, really grave crimes, but well that's a controversial view. I know high-ranking political people (who do not belong to any kind of ultra-right party) who have demanded such measures here in northern Europe and who have been accused of sleeping with the racists; it happened only the other week in a big city ten miles from here. But the real risks of having such lax checks on who is getting in weigh heavier than that, I reckon.