1) Let's look at the ship I am most familiar with, the NL Navy Zeven Provicien class (https://en.wikipedia.org/wiki/De_Zeven_Provinci%C3%ABn-class...). It generally would have 2 types of anti air defense missiles, the SM-2 and the ESSM (both US-built, see wikipedia for their publicly available specs). Apart from that, there are electronic and flare/chaff passive countermeasures and finally a Goalkeeper CIWS for last-mile defense. I have little doubt that we would have been able to take on an attack of 2 Harpoon missiles. OTOH, the Neptune missiles are a lot more modern than the Harpoon and modern missiles have been known to do tricky things like having a pseudo-random noise generator generate corkscrew like maneuvers to evade the defensive fires. I'll also note that the Moskva was built in the early 80s (though refitted after the fall of the Soviet Union) and it was apparently quite stormy (so additional radar noise from wave reflections may have been a thing). All in all, IMHO it seems quite likely that they were indeed hit. Warships don't just suddenly catch fire, and especially in warzones when the opponent has sophisticated anti ship missiles it seems more likely that the fire was caused by a missile impact.
2) For older warships it could be possible. Usually they would have a rotating air warning radar and a dedicated targeting radar for missile guidance. An example would be the STIR (https://www.thalesgroup.com/en/stir-tracking-and-illuminatio...) on NATO vessels, basically a powerful narrowbeam radar on a servo pedestal. There would rarely be more than two or three on a vessel, so it might be possible to distract all of them with several drones. Modern naval radars use active phased array technology where the amount of tracked targets is no longer the bottleneck (in practice, you'd need dozens of missiles), but as mentioned before the Moskva is from the early 80s so they would probably not have this yet. So it could happen, especially in a stormy sea where the waves provide a lot of additional radar noise, but it is really only speculating without a lot more information than we have right now.