1)Yes, the ATG is part of the Kozac sequence. You actually have a minimal Kozac sequence there, the full one is (GCC) GCC RCC ATG (G) the last G helps but is actually not entirely necessary either, though it is highly conserved, along with the R.
2) No, they don't need to be in multiples of 3, this is only necessary after the start codon so that they encode the correct amino acids. Having said that, with the use of recombination via the attB sites, there are special considerations with respect to frame, but I'm not sure exactly on those. So long as you copied correctly from the manual, there shouldn't be a problem.
3) You have done the correct thing and used the sequence from your plasmid. This will ensure that your primers are specific for your sequence and will work at the correct melting temperature. Don't worry about the bases I used - I copied those from somewhere else, not from your plasmid sequence. There is some wiggle room in terms of exactly which bases encode the various amino-acids in the HA tag, so different sequences can encode the same amino-acid sequence. To complicate things even more, there are different HAs for different species, so a mouse HA is different to a human HA. Use the one from the plasmid that you have!
The tag sequence you have given translates to YPYDVPDY, and it looks like you have copied the ATG, the GGC and the first 24 of the HA correctly from the plasmid as analyzed by Addgene, and annotated by the depositor. If you search for this sequence you will come up with it being the epitope for anti-HA antibodies. The sequence you have used for the Kozak is correct, and your start site is in-frame with your HA tag, so I am sure that you have the correct sequence and it will work.