[RPG] Does the spell Darkvision allow a PC to see through magical darkness

Well, if you don't mind making a pact with some powerful entity, you could get 2 levels of warlock. This will give you access to a few spells, some of which perhaps being interesting (both stats and flavor-wise) for your character. But most of all, this will give you access to 2 invocations.

One of these invocations should be Devil's Sight, which grants you the ability to see through any form of darkness, magical or otherwise, for up to 120 feet. This is more than enough to cover the 15 feet of the darkness spell. Cast it on your clothes, and bring terror to your enemies.

While this is a good strategy (generally favored by blade pact warlocks), it has some limitations. While under the effect of the darkness spell, your allies cannot see you. As such, any spell requiring line of sight that they would like to cast on you simply cannot work. Healing you might be problematic, as it requires your allies to be able to touch you. They might know that you are smack in the middle of that sphere of pure black darkness but, once they get inside, it's suddenly not so easy to find you anymore.

These limitations also affect your enemies, however. Any attack from the outside of the sphere should have disadvantage as your enemies, even if they can approximate your position, can't exactly see you to aim properly. Enemies inside the darkness should also suffer from disadvantage when attacking you, unless they possess some form of blindsight or a similar ability. When you attack them, you should have advantage on the roll since you are functionally invisible for them.

The biggest cost of this strategy is the fact that it requires multi-classing. While the lvl 19 and 20 abilities for monk would not really be missed (realistically, few campaigns will reach these levels), it will still set you back 2 levels in obtaining you other core monk powers. Note that doing this would get you 2 invocations, however, and that some of them can be quite interesting for a ninja-esque character:

• Armor of Shadows (cast mage armor at will, which might be better than using your wisdom for AC if its under 16),

• Eldritch Sight (cast detect magic at will),

• Eyes of the Runekeeper (allows you to read anything, even languages you don't know... useful for spying!),
• Gaze of Two Minds (share the eyes of a willing target, more spying!),
• Mask of Many Faces (disguise self at will!), etc...

TL;DR

Sacrifice 2 monk levels and multiclass as a warlock. Gain some minor but potentially useful spellcasting, as well as the ability to see through magical darkness and one more ability of your choice!

No, darkness doesn't cast a shadow.

At least, it doesn't without a particular DM making it a table rule — which would be a totally reasonable ruling to make. To tackle the question though, we must consider the default baseline from which such rulings would be made, avoiding assuming rulings that give us a result from circular reasoning.

Darkness not casting a shadow is non-intuitive, but magical darkness is inherently non-intuitive and operates by its own idiosyncratic rules.

I've emphasised the relevant parts of its effect description (PBR p. 86; PHB p. 230):

Magical darkness spreads from a point you choose within range to fill a 15-foot-radius sphere for the duration. The darkness spreads around corners. A creature with darkvision can’t see through this darkness, and nonmagical light can’t illuminate it.

The stipulation that it's effect is limited to a radius of 15 feet, and that its effect is to prevent illumination, not penetration of light, means that it does not and cannot alter light levels outside its area of effect.

Contrast this effect description of darkness with that of fog cloud: the latter's description simply says that it creates fog in a given area, and then leaves it as an exercise for the reader to extrapolate from our shared understanding of real-world fog — such as the fact that fog impedes the passage of light — with the help of the game's specific rules for obscured vision. Darkness, by contrast, does not try to leverage our intuitions about "magical darkness" — as none can be expected of us¹ — and instead gives specific effects. These effects are sufficient for most groups, so that groups who don't care (or who prefer a non-scientific fantasy experience) can get on with the game without having to tackle the question "but how does it work?!" with lengthy deliberations first.²

It could be argued that the line "A creature with darkvision can’t see through this darkness" means that light is entirely prevented from passing through. However, such an extrapolation would be a ruling limited to the ruling DM's game, as other DMs will not all also make the same ruling. (Since how darkvision operates is idiosyncratic and non-lawlike in the same way as how magical darkness does, we cannot reason from how it operates to how darkness operates, without a DM adding even more interpretive rulings.) Since such a ruling is an addition and not universal to all possible DMs, and because magical darkness is inherently illogical, that extrapolation can't be considered the default, baseline case.

^{1. Those of us who have a specific metaphysical reality in mind that does create intuitions about how magical darkness operates are precisely those who would want to make rulings about darkness in order to satisfy our intuitions and to make the spell better match our imagined setting. This is exactly what the permission to houserule, that the game gives DMs, is designed to accommodate. For the rest of us, the game doesn't assume anything, and gives us bare effects for things that are not transparent to the usual intuitions of modern humans, like darkvision and the darkness spell.}

^{2. In my own games, I'm likely to rule that it does cast a shadow because I tend toward classicism in my campaign metaphysics — if the issue ever comes up, which I expect it likely won't. Except that, if I'm running a romanticist campaign based on my ontological Chaos premise, I'm likely to say that it doesn't cast a shadow and neither does its contents, for no reason other than "because Chaos." So, there you go: it very much depends on the DM and campaign.}