multiplications per second for FIR filter
To answer your questions:


The number of multiplies is the number of taps times the number of sample per second.  Given a sampling rate of 300MHz and 31 taps, you will have to do 9300 million multiplies per second.
As Paul R says, whether a multiply can be done in one cycle depends on the processor.  Some can, some can't, and some appear to by having a long pipeline - once the pipeline fills, the result of one multiply comes out per cycle.  You would have to find out what processor you are using to determine how many cycles it takes for each multiply.  Also note, this varies also with the type of number you are working with.  Integer multiplication is usually faster, but can cause you other difficulties (it is harder to do signal processing with integers.)
As Paul R says, really only the multiplies are of interest since most processors have a combined multiply and add instruction.  If you are working with a processor without that type of instruction, though, you will have to remember to count the adds when budgeting your clock cycles.  Since there are as many adds as multiplies when doing an FIR, knowing how many multiplies there are also tells you the number of adds.