Every chat system since IRC has been worse than IRC. Without fail. Just use IRC, people, stop chasing shiny things.
Now all 3 of these could be implemented on a ICR server client. But they are not simple, not supported with all clients and not something that your marketing guy can easily use.
With hipchat/slack/etc they are all out of the box on minute-one and easy to use.
(b) Post links. Everyone in IRC has been doing this for 30 years. Works fine.
(c) Have your client log, or have a bot log to something with HTTP access. You can then use grep or a fancy web app or anything in between to search.
I'm with the parent. Scalable chat is a solved problem; it was solved in the open, via open source and open networks, over 20 years ago. Everything since has been focused not on the technical problems of chat but on the business problem of making money from chat. The fact that someone out there wants to make money on chat does not mean you need to give them money to solve your chat problems. Paying for things of value is fine, but in this case you simply don't need to. Sometimes the best things really are free.
This is not something "your marketer guy can easily use". And even for techies it has issues like lack of notifications (fixable), lack of non-suck mobile support, and, extremely important for me even if apparently not for some, typing latency (mosh is a partial solution but not good enough for me).
There are a few applications that use a daemon running a custom protocol to fix the scrollback issue: Quassel, Smuxi, weechat remotes, others. This is a decent approach in general, and the one that I use (weechat + Glowing Bear), but I haven't found any such applications with good mobile support or which are very high quality in general.
Maybe IRCCloud is the answer - has a spiffy web client and iOS and Android apps. It's a hosted service and non-free so I am not willing to use it myself, but most people don't care that much about such things, and it's not like Slack is any better on that front.
Disclosure: I work for IRCCloud :P