BIt of a Question and Answer session here These are to the best of my tiki knowledge, if someone else knows better, please post and correct me:
Tiki doesnt store access logs, however we had planned to use PhpOpenTracker and work was started but never finished, we need someone willing to take this on and complete the integration into Tiki, then I could answer yes!
Tiki allows you to have a custom home page, or a Wiki Home page. You could use the ARTICLE plugin to make a article sticky on that wiki page and include tiki modules too
Tiki has a since last_visit module I'm not sure if this is present in 1.7 but it certainly sitting in CVS code right now. as I use it on http://damiansworld.damosoft.homelinux.net
The documentation is current underway for v1.8 over at http://doc.tikiwiki.org, some features are done, others are in hand.