At present, how are they perceived by the people of Skyrim? By the general population, and by different factions?

really depends on what “present” is, but the most interesting answer is at the time of her death/as high king

general population: mixed bag. the years immediately following solvej’s coup were tumultuous, but at the time of her death things were actually a good bit more stable than they had been in recent memory, and skyrim was an independent province. shes surprisingly popular all things considered, but the majority of the population is neutral or negative towards her

she made an enemy out of nord nationalists, particularly in systematically eradicating the stormcloaks and in ceding the reach. her policies are largely conciliatory, with the goal of creating a united skyrim that can stand against the thalmor, and this is often interpreted as weak and placating. on the other end of that, she enforces her rule with the implicit threat of letting dragons go unchecked or intentionally setting those loyal to her on her detractors. and towards the end shes kind of spiraling and focused on becoming a living god.

anyway in terms of factions

thalmor: open hostilities

imperial legion: driven out of skyrim, some conciliatory measures, offered allyship against the thalmor

stormcloaks: wiped out

companions: outed as werewolves, some killed, but the people of whiterun liked them enough not to drive them out

thieves guild: pretty much unimpacted

dark brotherhood: pretty much unimpacted (i think they got a couple contracts against her, which failed)

college of winterhold: solvej used to teach there so its kind of awkward. the archmage, malae, does not like solvej’s whole godking thing but she doesnt seem to get the memo and puts a lot of effort into public works projects restoring the college and encouraging membership. so its like, alright i guess

How were they perceived before their Dragonborn identity became widely known?

solvej wasnt like, famous, but she was relatively known in a lot of places, partly due to being so conspicuous. she taught part time at the college of winterhold, and most people whove lived in winterhold, solitude, morthal, dawnstar longterm have seen her around and know her as “that big argonian” and someone you dont want to bother. 

HIHIIHHIHIHI MARI I HOPE U R TOO im ok rn i just feel kinda funky bc my eating schedule has been bad.... thinking abt shmoking to help the pain but i rlly dont want to move -_- look at winky now