Is it okay to keep on updating a published paper online?
Is it a good idea to upload a version of the survey on Arxiv and keep on updating it?


It's worth doing if you have the time and energy, but it's unconventional.  There are some continuously updated survey papers (such as the dynamic surveys in the Electronic Journal of Combinatorics), but the usual expectation is that a survey represents a snapshot in time.  As a career matter, writing a second survey on recent results a few years later may get you more attention and credit than updating your original survey.  Continuous updates can be especially useful if they are timely and the field is particularly hot, but they have their own limitations in a rapidly developing field (the original organization may weigh you down if you stick too closely to it).

From my perspective, the trickiest aspect is what to tell people.  If you silently update the paper, it won't attract as many readers as announcing that everyone should check back for periodic updates.  (And the whole purpose is to inform the community, so getting readers is important.)  On the other hand, it's difficult to commit to regular updates, and it's nice to avoid issues such as whether other authors should be unhappy that their latest results haven't made it into the survey yet.


  In that case, should the Arxiv version contain a note that an earlier version was published in so-and-so journal?


If you update the arXiv version of a paper after publication, it's critically important to be clear about how it relates with the published version.  Otherwise you risk confusing and upsetting your readers.

I would recommend against removing anything from the survey over time.  It would still be accessible via past versions on the arXiv for those who know to look there, but it's annoying to send a student to learn about X in Arani's survey and have them report back that it's not covered.