Does the client establish the TCP connection to the SSL terminator or
to the Webserver?
With SSL offload enabled the client makes an SSL connection to the SSL terminator, then the unencrypted traffic is passed to the webserver from the SSL terminator. If SSL Offload is disabled the SSL traffic is passed through directly to the webserver(SSL pass-through). Also note normally the webserver is setup to run on a different port than 443 (81, 8181, 4433, etc. to an internal IP or IPs depending on your configuration).
Does the SSL Terminator affect the TCP connection in any way?
Modification of the connection depends on the configuration of the SSL terminator. Example: If you enable analytics, deep packet inspection or stripping of detected malicious data or have certain rules setup to only allow the type of traffic you want, modifications can occur before traffic is passed to the webserver or passed back to the client from the webserver or SSL terminator.