Is it overheating?

Just to follow up on what Geeto said, It could also be that the bike is running slightly rich. This shows up with a hot engine because the hotter it is the richer it will run. That is why you don't use a choke on a hot engine. It is already rich enough. Now the causes of the richness could be caused by to big of jets(main and or pilots), dirty air cleaner, changed exhaust pipes, or too high of a float level. Geeto is right in that this is difficult to diagnose without seeing the bike. What do the sparkplugs look like when the backfires happen? Both the same? Dark and oily? Dark and sooty? White and dry? Light brown and dry? How is the ignition timing?
What do you mean by the gears stick? Is it hard to shift from one gear to the next while riding? Hard to find neutral at a stop? Hard upshifting or downshifting or both?
What makes you think it is overheating? Bad smells? Discoloration of the headpipes?
Lots of questions to be answered before a good diagnosis can be made.
Let us know,
Ken

AHRMA 412
Vintage racing - old guys on old bikes

Ok, as far as the shifting into neutral goes, that is the usual thing with Hondas of this vintage. It is generally caused by the clutch heating up and dragging a little bit. You may be able to cure it for a little while by replacing the clutch plates, both fiber and steel, and very meticulouslly adjusting the clutch within an inch of its life. This might cure it for 20 minutes or so. The easiest cure is to learn to click the tranny into neutral as you roll into a stop while the bike is still moving. It becomes second nature after a while. As far as the trans dropping out of second can be caused by a slightly bent shift fork or a less than positive shift into second and a weak shift drum detent arm spring. Try being very authoritative in you first to second shifts and see if that helps. If it does then the shift drum stopper arm detent spring is suspect.
As far as your backfire issues go, put a new set of plugs in it and ride it around until it shows the symptoms and then pull the plugs and tell us what they look like( see my previous post).

Ken

PS what oil are you running?

AHRMA 412
Vintage racing - old guys on old bikes