1. Neither. FreeS/WAN is completely different from the built-in PPtP. FreeS/WAN provides a full-time WAN VPN between two LANs via the Internet, whereas PPtP allows ONE machine to participate in the remote network (oversimplified, but there it is). Once FreeS/WAN is set up, ALL nodes on both networks will be able to access all other nodes. (NetBIOS browsing is iffy.)
2. Yes, a FreeS/WAN link will "combine" your home and office networks. I have this running on SME 5.6 machines for a couple of WANs: one office even uses it as, among other things, a "remote copier" that scans a document in Louisiana and prints it in Minnesota. Spiffy! It works best if you have static IPs at both ends. FreeS/WAN is unforgiving in initial setup but extremely robust once running.
3. More information needed: have you set it up so that the SME box is the only one connected to the Linksys router, i.e. there's another switch or hub "downstream" of the SME box on the LAN side? Or is the Linksys a wireless router? Have you told the SME box to hand out the IP of the Linksys as the default gateway? I assume other machines on the LAN don't have this trouble. What happens when you set the TiVO's IP, DNS & gateway manually?
Be as specific as possible when asking for help unless you're wearing your asbestos underwear!