These were available starting around 1980 or maybe a little later, and were a fairly popular model, lasting (I think) about 8 or 9 years in the marketplace. About 54cc, but nowhere near the performance of a European saw, due to the reed valve induction system and conservative porting. The engine was fairly torquey at lower rpms, therefore a little more forgiving to use for inexperienced operators.
The chain-oil pump is a crankcase-pulse driven diaghragm unit that puts out almost enough oil on most units. The pulse line can rupture or crack, causing air leaks, as can the diaghragm. The carb clamps down over the end of a rubber manifold fit into a mounting plate above the fuel tank and crancase. About all brands have some rubber parts failures eventually, and Homelite is no exception. Check this out, too.
I have no idea if parts are available, but Homelite used to have a pretty good rep for parts. Since JD sold them off recently, that may change.
As a Kid, I used Homelite saws a lot, then changed to Echo just before I figured out that if I wanted to earn a living and retire, ever, I would need to get out of the woods, and learn a real trade. (No offense, full-time arborists and loggers). Anyway, whilst going to school, the opportunity to make some cash presented itself, but I needed a chain saw; lo and behold, a 330 was found at a yard sale. I used that saw hard and long, cursing at it endlessly...I had troubles with it in hot weather, and You might as well keep it in your nice warm bed and start it there if the temp outside falls below about 20 deg below, farenheight, but aside from that it helped buy me beer and cornflakes for a while.