The timeline of the X-men movies is pretty complicated, especially with the introduction of Days of Future Past, and alot of events don't seem reconcilable with each other. However, with a little (ok, a lot of!) creative trickery, I've managed to construct a timeline that explains pretty much everything.
So, first off, I would use First Class as the basis for the timeline. Eventhough this movie was not produced first and actually caused many disruptions in the timeline, it is chronologically the first. So Charles and Erik met in 1962 when they were ca. 30 years old (I think the producers have said they are around 28). Bryan Singer himself said, "(...)in X-Men 1 I personally wrote the line that of course I now regret: ‘When I was 17, I met a young man named Erik Lensherr’ and then in X-Men: First Class I changed that!” so we can forget that line. Charles lost the use of his legs in the Cuban Missile Crisis, 1963, at the hands of Magneto and they parted ways there and then.
I am guessing that one of the problems in the timeline that you are referring to is the fact that, in the beginning of Last Stand, we see a flashback to the 1980's (according to my calculations, between 1984 and 1986) in which Charles and Erik (played my Stewart and McKellen, with amusing digital facelifts, not McAvoy and Fassbender) are seen recruiting Jean Grey for Xavier's school. In the Flashback, Xavier is able to walk and on friendly terms with Magneto, although First Class shows us that they parted ways 20 years ago. Charles also had his telepathic ability.
Firstly, the question of Charles' ability to walk is quite easy to settle after the introduction of DoFP to the timeline. We know that in 1973, 10 years after Cuba, Charles was taking a serum that gave him the use of his legs but, due to his taking too much of the serum, it took away his telepathic powers. In the altered DoFP timeline, in which Logan travels back in time to the 70's, it is Logan who succeeds in weaning Charles off the serum. But in the original timeline, since Logan was never involved with Charles, he could easily have continued using the serum well into the 80s and perhaps even beyond. Since it was only the high dosage that stripped Charles of his telepathy, it is concievable that he simply lowered his dosage so that he could still walk but retained his telepathy. Only in later years did he finally sumbit to life in a wheelchair.
The issue of Magneto and Professor X being friends in the 80's flashback can only be solved by pure speculation. I seem to remember that, in the antimated series of X-men, and, I believe, also in the comic books, Magneto and Charles crossed paths several times, sometimes working together, sometimes against each other. The same thing goes for the movies; for example, in X2, Magneto works together with the X-men... to an extent. So it is definitely possible that Erik and Charles joined forces again in the 80's, and seperated again due to ideological differences.
As for Cyclops existing in the Wolverine movies, you're simply confused as to the time period. The movie is set in the 80's, not the 60's. Oh, and Cyclops and Havoc aren't brothers, as far as I know. I don' think it was ever stated that they are, and Havoc being Scott's much older cousin or uncle is far more plausible.
And last but no least, the girl in Wolverine- Kayla's sisters who displays similar powers to Emma Frost- that so many think is Emma Frost is actually a completely different character, according to the movie's crew. It's strange that they have exactly the same powers, but stranger things have happened in comic book mives, right? Maybe they really are related... Either way, both Emma and and Kayla's sister are minor characters, and I think that, in the great scheme of things, their similar powers are only a minor grievance. Also, I doubt it will ever be explained, so it's probably just something we have to make our peace with.
Other than that, I can't really find anything in movies three and four that is completely out of synch with the timeline. Naturally, there is the matter of Xavier's survival at the end of Last Stand, but that is a whole other thread...
I hope that I could help shed some light on your question and that you are satisifed with my answer. If there's anything else, let me know :-)