The PLSS had silver-zinc batteries, yet I believe that the batteries were exchanged rather than recharged. Are there reasons not to recharge them on Luna? Or am I mixing battery technologies?
I'm reasonably certain that these were the non-rechargeable type, and rechargeable variants didn't exist back then. There weren't many rechargeable battery technologies available at all... possible only lead acid (heavy, though that's less on an issue on the moon) and ni-cads, which were a bit rubbish. Your moon base would presumably have to use one of these.
You could always use tethers for most work, and a more substantial power source like a fuel cell on a buggy.
The PLSS also had lithium hydroxide CO2 scrubbers. Would a regenerative system have been possible at the time?
Possibly, but the chemistry required to get your lithium hydride back isn't terribly difficult so it could be recycled. This may be simpler than trying to use other rebreather technologies, certain in the era you're considering.
Could the coolant water have been recovered?
Probably, but the coolant system does have a limited lifespan, I do believe. I'm not sure how practical cleaning and refurbishing it is, nor do I know if there was a reasonable alternative available Obviously one was never engineered, because EVAs in earth orbit can get fresh kit easily enough, but that's not to say that it was impossible and maybe some investigation of old-school manned mars mission plans might bear fruit. NASA are working on a replacement for the current version of the cooling system for longer term usability.
And the one where I'm really stumped, what would regolith do to the fabrics and seals? Could they be dusted off easily, or would a few use cycles start abrasion.
Moon dust ruins everything. Seriously. This stuff might be the thing that renders your moonbase (or mars bases, for that matter) impractical and unsustainable. The stuff is sharp, hard and chemically reactive. It'll abrade fabric and degrade seals and it is toxic to boot. You'll get loads of problems with static. I'll bet it absolutely won't just dust off easily, and even if it does it'll hang around to ruin other things including your health.
I think there's some recent research done on ways to overcome this (using double-shell spacesuits, and sintering dust around your base to reduce exposure risks, for example) but I don't know how far back this research went (and I can't find relevant NASA papers right now, but I'm sure they'll pop up soon enough). I seem to recall there was some relevant research back in the day, but I can't seem to find the right search terms for a useful answer. In any case, this is clearly the major issue, as you've already spotted.
dhinson919 kindly supplied a link to The Effects of Lunar Dust on EVA Systems During the Apollo Missions, over 60 pages of Bad Things and complaints associated with moon dust, including a load of relevant quotes from the astronauts themselves. Particularly relevant:
Pete Conrad’s suit, which was tight before the first EVA, developed a leak rate of 0.15 psi/min after it, and rose to 0.25 psi/min after the second EVA. Since the safety limit was set at 0.30 psi/min, it is doubtful whether a third EVA could have been performed, had it been scheduled.
TL;DR: the stuff got everywhere, it was very hard to remove, attempts to reduce abrasion damage were apparently partially successful but issues with seals remains and only the limited number of EVAs and short duration of the trips made this acceptable. This seems like absolutely the number one issue you're faced with. It isn't at all clear to me how capable 1960s technology was at ameliorating these sorts of issues.
Could the body waste subsystems be laundered?
Would you even need them? Just pop back to base and poop on an actual toilet. Luxury undreamed of for the Apollo peeps.