I haven't had a chance to see the show yet (which is sort of inexcusable, because I did a little informal consulting for them early on — things like "what did the first samples of plutonium look like and how were they shipped"), but:

1. The entire point of Los Alamos being where it was was to keep the scientists isolated. It was security through isolation. They had limited access to nearby towns (e.g. Santa Fe) and could take vacations (e.g. for a few weeks) to go to other parts of the country. The high-ranking scientists had more extreme demands made upon them than the lower-ranking ones (Oppenheimer could not fly in an airplane, for example, and had a "bodyguard" who was also keeping tabs on him). But the goal was isolation, and they were not supposed to tell people where they were and what they were doing. The fact that they were even working on a secret project was itself a secret (which is an usual situation).

2. Yes. Some more and some less than others, of course. It is difficult to generalize, but frustration about secrecy was a common complaint. One of the main differences between a place like Los Alamos, though, and other secret sites like Oak Ridge, is that at Los Alamos most of the scientists knew what they were working on, at least. At Oak Ridge, almost nobody even working there knew what the point of the plant was, and that created all sorts of morale problems.

3. Yes. Los Alamos was initially going to be completely run by the military and all scientists would have to become commissioned officers. Oppenheimer was originally on board with this but several scientists convinced him this would not work — they opposed military-style chain of command and bureaucracy, because it meant that lower-rank people could be commanded about by higher-rank people, and that was, in their mind, not in the spirit of science (where the lowest-ranking person can still be more correct than his boss). Eventually it evolved into the system where there were civilian workers (technically employed by the University of California and working ultimately under Oppenheimer) and military workers (members of the Army Corps of Engineers and headed by a military officer). Sometimes the functions could be blurred — the Special Engineering Detachment, for example, were military men (who had to sleep in barracks, march around, wear uniforms, and all that) who did engineering work to help with the scientists.

4. During World War II the real concern was with leaks and not espionage, at least not the kind we think of today. They were worried about scientists talking to the press, or the press finding out about it otherwise, and breaking the secret open before it was ready. They were also worried about enemy spies (e.g. Germans) trying to find out about the project. They weren't as worried about moles — scientists inside the project contacting agents of other states — as they in retrospect should have been. This was in fact the major security problem during the war: there were at least three Soviet moles inside Los Alamos (Klaus Fuchs, Ted Hall, David Greenglass). There ended up being essentially no effective German espionage on the subject. (Ditto the Japanese.) A lot of the security issues that the military people spent most of their time worrying about ended up looking quite trivial in retrospect, e.g. whether the British violated the Quebec Agreement in making some postwar commitments to a few French scientists who were working at Montreal. Sometimes the security people like to pretend, in retrospect, that they were really concerned with Soviet spies, but this is mostly a Cold War point of view projected backwards (there was some concern about Soviet activity the UC Berkeley Rad Lab, but it was considered a minor threat). The biggest security disaster they could imagine is the press getting ahold of this, the whole thing being talked about in front of Congress (who were largely out of the loop), and thus alerting the Germans and Japanese and Soviets and everyone else that the US was spending a lot of effort on making an atomic bomb.

There are many sources one could read to follow up on this (#1-3 are covered in most popular books about Los Alamos, for example, like Rhodes' The Making of the Atomic Bomb or Conant's 109 East Palace; #4 has a more spotty literature that is mostly focused on spy stories — I am currently working on a book about US nuclear secrecy that I hope will make a major contribution to this literature).

I addressed several of these questions in a piece I wrote for Popular Mechanics. http://www.popularmechanics.com/technology/digital/fact-vs-fiction/what-manhattan-gets-right-and-wrong-about-los-alamos-17033716

If I recall, Surely You're Joking, Mr. Feynman has a few dozen pages of life at Los Alamos. Censorship of letters is mentioned along with a bit of friction with the miltary brass.

Edit: I should note that, as /u/restricteddata has pointed out, Richard Feynman wrote the book, where the premise is a series of anecdotes about his life, and likes to inflate his ego somewhat (it's a great read, though-really). So keep in mind there's a bias.

I have not seen this show Manhattan, but based on what I do know about the Manhattan Project, points 1,2 and three would be accurate if they show the scientists being sent to Los Alamos, New Mexico and show General Leslie Groves as an abrasive figure. Los Alamos was a remote location, in the middle of a sparsely populated state. It would be easy to understand if the scientists felt they were leading a cloistered life and their families chafed at their confinement and isolation.