Does Analog show referrals by search engine without having to define search engine URLs to it.
There's a guy who who does this for you so all you have to do is download a text file when it's updated (Israel Hanukoglu's SearchQuery.txt [science.co.il] file) I've made a few contributions to his list...it's pretty comprehensive and updated at least once a month...
Does one have to list all common spiders and spider sources in order to know spidering details.
No, it will simply tell you what spider have been visiting you...it's up to you to find out what they are. There are some good ROBOTINCLUDE suggestions in this thread [webmasterworld.com]...and I think there are a few more here I can't immediately find.
Does it show "time spent" on web pages
There may be a way to do this, but I haven't used it.