'Now, i recently got an old Mac for my college work.' ... unlike PC'ers, Macintosh owners / users do not identify their computers as a 'System 9.2.2' or 'MacOS X 10.2.8' computer; instead they state the explicit model - 'iMac G5 20 inch', 'Mac IIci' ... running System 9.2 ... Thus, 'old Mac' is non descriptive, non informative.
'But, will i be able to share files with the windows computers?', yes ... 'And how?', Dave.
If you 'old Mac' is a G3 Mac with built in USB ports, you could install either 'Jaguar' (MacOS X 10.2.x), 'Panther' (10.3.x), or (cough choke gag ...) 'Tiger' (10.4.x). With MacOS X installed 'Dave' may be more of an option, than a requirement - as with 'System 9.2.2 or earlier' installed.
'Is it possible to put another network card in my PC, and run a Lan cable from the PC to the Mac?', anything is possible - not all is probable. Once Dave is installed and configured on the Mac, the balance of the configuration would be performed on the PC. A subject supported on Window's support web sites, etc.
'Would (the) internet work (that is, be accessible) on my Mac that way if the PC is on?', the PC would have to be ON.