I buttered the bottoms and both sides of each brick when I laid them, but I did not custom cut the majority of my bricks. I look at mortar as just being a solid space filler that mimimizes the possibility that a brick can move in any direction. I may be totally wrong, but I believe the actual bond strength of mortar to brick is very very low. Therefore, at least in my small mind, full mortar joints reduces possible brick movement problems related to thermocycling. (That said, you could easily make an arguement for leaving spaces to allow for brick expansion/contraction and I might believe you
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Make sure that if at all possible, you don't allow mortar joints to line up anywhere between rows. Almost all my cracks occurred at areas where the mortar joints were within an inch or so of the next row.
As far as the existing gaps in the mortar, I'd make a wetter mix and finger it into those voids, or spend 5 bucks on a grout bag and attempt to force it into the bigger ones.
The lower courses are almost vertical, so it may be that their strength due to the sheer weight of the bricks in a downward didrection will not be affected by voids, especially if you use cladding on the outside. There's a couple of discussions in this forum about failures of arches. If memory serves, it's somewhere in the middle third. That is where I'd get serious about structural integrety. - my advice, to be taken with a grain or two of salt.