How to migrate from ArcGIS for Desktop to QGIS?
To be honest the time frame you mentioned for the migration sounds really tight, especially if you want to research, test, evaluate and deploy!
We have recently migrated from using ArcGIS as our desktop client to QGIS. While everything you have mentioned sounds possible the biggest issue I have found is managing the storage of Raster datasets, but like Nick mentioned earlier I too am waiting for PostGIS 2 to solve my problems there!
We created a "functionality matrix" and I believe you should do this as well at some stage. What we did is over a period of time (1-2 months) was create a list of tools from the geoprocessing toolbox and ArcGIS application that we used to achieve our daily tasks. Then we spent time replicating these tasks and searching for these tools in the QGIS application, we simply gave the task a tick if it could be done in QGIS or a cross if we couldn't do it. If it couldn't be done we then looked for alternative ways to achieve the same results.
We have now employed QGIS as our desktop GIS client, but this method gave us a clear idea on whether or not QGIS was a viable option. To be honest I think it is quite suitable desktop application with a strong and active community. I believe paired with PostGIS it is as good as our previous ArcGIS, ArcSDE/Oracle combination!
Make sure you test vigorously, document your challenges and ask lots of questions here and on the QGIS forum during your testing.
1) Analyse the areas outlined with the polygons and added buffers to some of them.
Buffers are supported. For further help, we'd need to know what "analyse the areas" means.
2) Answer questions like: Does this kind of fish (represented by a layer of points) always occur near a certain rock type (represented by polygons or points).
You can check if there are fish points outside the polygons.
3) Add new seafloor images (as new layers) representing the same area, but taken at a later time, to see if the distribution of features in it have changed over time (i.e. there's 15% more fish, etc.).
No problem.
In the future, we would like to add bathymetric data so that we can make a 3D view of seafloor represented by our images.
Some work has been done to include 3D viewer into standard QGIS distribution but it's still far from production quality. A serious supporter would be helpful.
Can the above be successfully migrated to QGIS and HOW do I do it?
If all your data files can be read by OGR/GDAL, you shouldn't encounter any problems. (Which formats are you using?) Simply give it a try. It really shouldn't take much more than an afternoon to find out.
As you say yourself I think all this can be done in QGIS.
If not, just use some of the saved money to pay someone to fix it :-)
that is the most important part of open source. anything is possible.
you might also want to look at storing your data in PostGIS. when postgis 2 is out you will have rastersupport in the database and you will be able to do a lot of raster analysing directly in the database. and show the result in qgis.