Nicotine is very bad for you, without regard to its symptoms and side effects, it gets through the blood/brain barrier, makes a home in your nicotinic acetylcholine receptors, forces your brain to up-regulate these receptors to the tune of 8X(!) to ensure that it has a place to stay permanently.
It creates dopamine pathways in your brain which link positive memories about smoking to every aspect of your life, making you forget how calm and lovely life was before nicotine, and artificially activating your flight/fight response mechanism every time the nicotine level begins to drop.
It's very, very harmful and makes permanent changes not only to your brain, but to your genes. Nicotine users have some genetic "switches" flipped on irreversibly.
Gum and patches are just designer nicotine drugs. They are more of the poison from the same people who sell cigarettes and snuff. Stay away from all forms of nicotine for great justice!
I used to smoke a pack of unfiltered camels a day for 7 years. I had sleep issues where I would sleep lightly and often wake up super early and need a smoke. I would go back to bed for an hour or so and sleep poorly and have a really hard time getting up when the alarm goes off. Really affected my school work- I got to the point where I needed to nap as soon as I got home. I could down energy drinks and just get more tired.
So yeah, it's a stimulant and it does make it harder to fall asleep. How much so depends on the person - but studies show there is definitely a connection between tobacco use and sleep problems.