Any plates will do. There is a lot to consider though. Evaporation of media is a serious problem in these assays. There are a couple good publications on this. Some have developed enclosures, little home-made humidors to keep this from becoming an issue (http://www.ijastnet.com/journals/Vol_2_No_6_June_2012/4.pdf). Do a test for yourself, seed a 96-well plate, let it incubate for 24-48 hours, then measure the media volume in each well. Amazing differences based on position in the incubator, position of the well (edge effect), etc. One option is to replace the media prior to your addition of the alamarblue assay reagent. Of course, be careful not to let the wells dry at all during the media replacement. Another good idea is to randomize both seeding of cells and whatever treatment the cells have undergone.
Any plates will do. In case you are using 96 well plates it would be good to just add PBS to empty wells and the well around the rows where you are seeding to cut down on the error due to any evaporation from the edges.
Depends on your cell doubling time. We usually do a cell count with any new (esp primary cell line) to figure out the kinetics. Also, time of incubation with dye varies significantly with cell type and density (15min up to 4hrs).
As for your original plates query, Alamar blue can also be used for fluorescence (more sensitive) and absorbance.......we tend to transfer probed/conditioned media to black strip wells for former. The only caveat for the clear plates for absorbance is to ensure they are flat bottomed.