Spidermonk, spidermonk, does whatever a spider/monk can…
We have a monk 6 (Way of Shadow) / druid 2 (Circle of the Moon) Wild Shaped into a Giant Spider. Looking at the rules, this is how I think things would work:
1. The monk has a Wisdom of 16, so Unarmored Defense gives her an AC of 16 in spider form. This uses the spider’s Dexterity (+3) and her own Wisdom (+3) which she retains in Wild Shape. She doesn’t get to add the spider’s natural armor because she’s using an alternate method of calculating AC.
2. When she takes the Attack action, she can attack twice due to having Extra Attack as a monk feature. Each of those attacks can use either of the spider’s attacks (Bite or Web) or can be an unarmed strike using her d6 monk damage. So she could take the Attack action, shoot a web, then close in on her target and bite it.
3. Instead of Web + Bite, the monk could use Web + unarmed strike. Then, because the monk was unarmed and used the Attack action with an unarmed strike, Martial Arts lets her take an additional unarmed strike as a bonus action.
4. The monk is not proficient in spider webs or bites, so when making either of those attacks she would use the spider’s attack bonus of +5. For an unarmed strike where the monk has proficiency, she would use the spider’s Dexterity of +3 (rather than Strength, due to Martial Arts) plus her own proficiency bonus of +3 for a total attack bonus of +6.
5. The monk has Ki-Empowered Strikes, so her unarmed strikes in spider form count as magical, but the Bite attack does not (it’s not an unarmed strike).
6. In spider form, the monk can use Shadow Step to teleport as a bonus action. The spider form has blindsight and can perceive 10′ in magical darkness, but the monk could not use that to teleport because Shadow Step requires a target space you can “see”.