Some answers at Math Overflow as (former) user122276:

https://mathoverflow.net/questions/391931/which-representations-of-mathfraksl2-are-homomorphic-images-of-the-tensor/392578#comment1025085_392578

https://mathoverflow.net/questions/385099/when-do-flat-holomorphic-connections-exist

https://mathoverflow.net/questions/123942/how-many-flat-connections-has-a-line-bundle-in-algebraic-geometry?noredirect=1&lq=1

https://mathoverflow.net/questions/390179/an-almost-complex-structure-on-the-real-n-sphere-sn

https://mathoverflow.net/questions/55244/why-must-nilpotent-elements-be-allowed-in-modern-algebraic-geometry

MSE: What is a "moduli space" in math/physics?

What is the definition of moduli space, in math vs in physics?

Some answers to "bountied" questions:

Motivating (iso)morphism of varieties

Why do we use divisors in algebraic geometry?

Is there a theory that describes eigenspaces of matrix functions near degeneracies?

https://math.stackexchange.com/users/858083/hm2020?tab=bounties

Answers to algebraic geometry questions:

Transition maps of vector bundle $\mathbb{C}^{n+1}\backslash\{0\}\times\mathbb{C}/\sim$ over $\mathbb{C}P^n$.

A description of line bundles on projective spaces, $\mathcal{O}_{\mathbb{P}^n}(m)$ defined using a character of $\mathbb{C}^*$.

Why is the projection map $\mathbb{A}^{n+1}_k\setminus \{0\} \to \mathbb{P}^n_k$ a morphism of schemes?

Representations of an algebraic group $G$ versus representations of the group $G(k)$

Distributions of a group scheme as differential operators.

Abel map on the symmetric product: why it is locally boundedness and holomorphicitiy

Grassmannian $\hbox{Gr}(2,\mathbb{C}^5)$ is homeomorphic to $\hbox{Gr}(3,\mathbb{C}^5)$

Genus Degree Formula for Curves over Arbitrary Fields and a Reference Request

A question on varieties and morphisms of varieties.

Grothendieck point of view of algebraic geometry