After checking out the weapon lists for both games, there is one more pistol (Walther P99), three more submachine guns (Type 05, Steyr AUG Para, and Scorpion VZ83), four more assault rifles (AKS-74u, Barrett M468, FN FNC, and Enfield L85A2), two more sniper rifles (Heckler & Koch PSG-1 and Accuracy International Arctic Warfare), and one more shotgun (Mossberg 500 Tactical). The number of light machine guns stays the same. Additionally, all of the guns in the first game carry over into this one.
Going up ranks is not too bad because of the new ACES system. The ACES system gives you points for different achievements in three categories, with the categories being Marksmen, CQB, and Assault. Getting a headshot gives you one point in Marksmen for example. Another example is a kill with an explosive nets you two points in Assault. Originally, there was just 20 levels to the three categories and each odd numbered level gave X amount of experience; each even numbered category gives a weapon. After an update, the system stayed the same, except every level over 20 gives 5000 experience.
Time to get the UMP? I am assuming you are talking about the H&K UMP45? If that is the case, then it is gained at the 4th level of CQB, which does not take long at all to achieve.
Every kill in single player nets you experience. The amount of experience gained depends on which difficultly you are playing. You also gain experience from each kill your teammates make, though the amount is less than what you get for a kill. I just restarted with a fresh game not too long ago, have not spent a bunch of time playing, and I am already at the 17th level of Marksmen, 9th of CQB, and 11th of Assault and have a rank of Gunnery Sergeant (8th rank).
I cannot really comment too much on the lag of the first game compared to the second because I did not play the first online. But like any game, there are games you will get into that lag and others you get into that do not.