Well the crash right after you connect thing happens moastly when i swich servers or when a new map loads. It never happend the first time to me.
The connection problem is probably LAG or server crash. You should recheck the internet settings of STEAM.
About the crash problem all i can advise you is that you try a fresh install of ESF. Or since you said that only happens recently maby its asociated with the latest STEAM update. There is a file in your STEAM directory that has the extention .blob delete that and let STEAM reupdate.
ok thats all fine and dandy, but the question remains. i bought counterstrike, the 14.95 package, off of steam. now am i able to play esf from this purchase, or do i need to buy half life as well. because there is no way to install half life without buying it.