If you want the dimensions and grid of the aligned EPI to match the anatomical reference, use -master_epi BASE. If you want a different voxel size, then you can also use -master_epi_dxyz 'nn' to set the voxel cubic dimension to a particular size. Note EPI output at what is usually the fine grid of the anatomical data will result in a very large dataset, as you have seen, and is usually not very useful.
You do not need to apply the matrix on your own, though you can if you want to. The aligned dataset is one of the outputs of the script. If you are doing the epi2anat alignment, it will share the same name as the original but have the suffix appended.
For visualization of the alignment, you can use the -AddEdge option for align_epi_anat.py and the AFNI GUI.