In my experience (10-12 years many years ago and 2 recently), horizontal pressure can sometimes cause an already sticky valve to hang, but again it should not have happened from day one on a new horn. There is always some horizontal pressure from right to left when you play, but I doubt that worrying about that will do anything but mess with your playing. Don’t worry about it.
Oil residue is a good theory. Maybe the horn had been sitting around for months with old oil in it, but they shouldn’t have let it out the door without checking it.
It sounds like you have never cleaned it and have had no instruction on how to do it properly. If YAMAHA did not include any cleaning tools or instructions with it, go to their website –I’ll bet they have videos or instructions there. If you follow their instructions it won’t be likely to affect the warranty.
I’d be more concerned with the fact that it never worked right than trying to fix it now. It’s unlikely that you did anything to cause the problem. You might have added more residue to what was there, but (as you said) it never worked right. It might be something mechanical.
Post your original message on the Trumpet Boards and some folks who deal with things like this every day will give you more suggestions. For free — this is not an advertisement (LOL).
Remember, the store you brought it from will have a Yamaha rep they deal with and might well be the easiest way to deal with Y.maha