Word...the stock mixing tools in Fl are a great starting place but be sure to look into outside plug-ins that are just a little bit more advanced in what they can do for your tracks.
Yes you and mix and even master in FL Studios. Now as for what plugins to use that a whole another story! There no set rules that state which plugins should be used on which tracks. Hit-up Youtube and search mixing+Fl Studios.
I mainly use FL to mix, sometimes I like to try and stay sharp by exporting the stems to Reaper and starting from scratch though. I'm curious though if anyone has a mastering plugin that they've found to actually be decent? I'm hesitant to rely on a plugin to do the mastering work
its possible. a good master requires a great mix. i master with ozone 4 because it has everything you need all in one plugin..so yea its possible, also it helps alot if you track out all of your sounds.
Of course you can mix/master in FL Studio. But don't think of it as a process that occurs at the end, you should be fine-tuning and adjusting things to flow evenly throughout your project, to make the end far more easier to sort out, if even necessary. Most basic way to do this is just sorting of volume knobs, next you'll start needing to use stock FL plug-ins (or external if you prefer) for EQing. Maybe even something like iZotope Ozone on the master to get a certain sound at the end.
Your question was kind of funny because mixing and mastering is a totally different thing. But to answer, yes FL is good for mixing and mastering. But it's a different thing if the FL plugins are good. Pretty much only plugins I use from FL is EQ, that's it. For compressors etc. I have other plugins.
PS. If you don't know the differences between mixing and mastering, please read and learn from this forum or somewhere else. Too many people confuse these things and then ruin their songs with bad mastering. Just as a tip to you