I won't be the one to provide an exhaustive list of what pharmaceuticals aren't/are allowed. You're aware that pseudoephedrine isn't permitted and are considering taking a version of sudafed that contains Phenylephrine HCl instead. In the very unlikely event that your medicines are queried this seems like an entirely sensible explanation to me. Worse that can happen is that it gets confiscated and that you'll need to go to a chemist and get a Japanese decongestant for the week. I can't really see that happening though.
I'm not one to take pills and potions around with me and the only medicine I've taken in Japan has been what I've purchased there. I'm more likely to bring back cough sweets from Japan than take anything with me. If you're that bunged up whilst you're there you can show your cultural sensitivity by wearing a surgical mask (the tip from guidebooks about blowing your nose being taboo is baloney, just show the same restraint you'd like others blowing their nose in your proximity to show towards you).

I've never used KIX just Nagoya and Narita. The level of questioning has always felt appropriate, search dogs are common so I would resist the urge to take explosives and recreational narcotics or drugs that don't conform to an expected amount for a 6 day trip. Only time I felt the questioning was intrusive was past Customs one time when I was helping out a gormless ex workmate of my husband who happened to be on the same flight as me, because of her I ended up hanging around the airport much longer than I usually would.

Too cold in January?

It might snow, then again it might not. The biggest dilemma is which shoes to pack. Something sensible that can deal with icy slush but that you can take off easily as shoes need to be removed in a great many places. Watch out with synthetic clothes as the air is dry and static shocks are common at this time of the year. And take clean pairs of socks everywhere in case the ones you're wearing get wet or smelly. (Oh yes, most deodorant in Japan is ineffectual, don't forget to pack some)

Carry on only? You could but you'd need to stay away from mountainous rural areas. I've been to Mt Takao on the outskirts of Tokyo on New Years day where it started off fine only to snow a great deal while we were up there. And we'd thought all those people in heavy hiking gear were over dressed on the way up, we realised we were horribly under dressed on the way down. So, no. If you want to venture out of the cities, carry on only isn't enough.