For general information on what maintenance needs to be done, and when it needs to be done, you need to refer to the Honda maintenance schedule contained in the Owner’s Manual. Nobody knows more about how to properly maintain the car than the folks who designed and built it, and they have imparted their wisdom in the manual.
As to the tires, 45k miles on a set of original equipment tires is actually very good. Typically, OE tires are not of the highest quality, and thus may last only 25k to 30k in many cases.
In any event, a visual inspection of the tires by you should prove to be very informative.
Are the tire treads worn evenly across the width of the treads, or are they more worn in some areas than others? Uneven tread wear is usually the result of a need for wheel alignment, or tires that are not balanced properly, or worn components like struts, ball joints, tie rod ends, etc. Worn components are not likely after 3 years/45k+ miles, but this is not impossible.
Are the wear bars beginning to show on any of the treads. This is a horizontal bar running across the tread. Once this bar is even with the rest of the tread, it is time to replace the tires. I replace my tires before this happens, as the ability of the tires to resist hydroplaning on a wet roadway are severely diminished as the tread gets more worn.
Did the service folks give you any information on the most recent service invoice about the amount of tread remaining on the tires? This is usually expressed in tenths of an inch or twelfths of an inch–as in 3/10 remaining, or 4/12 remaining.