OK, I'm definitely not an expert on ionosphere physics but since nobody bites...
a) High solar activity is generally beneficial for MF/HF propagation because it increases F and E layer ionization which makes reflections from these layers stronger.
So far correct but to apply this broadly to MF and HF isn't really helpful: What the higher ionization does is increasing the MUF (Maximum Useable Frequency). MF is always far below both the MUF and the critical frequency (at which vertical incidence signals still get reflected), even in the worst case - winter in a solar minimum.
Upper HF propagation only occurs when solar activity is high.
No. Well, depends on what you call "upper HF".

Upper HF propagation occurs as long as the the MUF is just high enough to allow refraction of waves hitting the F-layer at a very low angle of incidence for a given frequency (the MUF is decreasing when the angle of incidence increases until it is = critical frequency). Surprisingly, this is almost always the case even with the lowest solar minimum flux indices (SFI <70) for frequencies up to 20 MHz and that can sometimes reach 28MHz when the flux increases just a little (e.g. SFI >70)...
as long as the ionosphere is undisturbed and the geomagnetic indices stay low.
However, since both the signal strengths and the incidence angles are low in these very baseline propagation conditions, this can be observed only in optimal reception conditions (zero local noise, low receiver noise, high antenna gain/directivity/flat takeoff angle). If any of these conditions are not met (which is the case for most of us at home), the band will appear "closed".
Here's a video shot under this kind of minimum (zero sunspots) conditions (SFI=70, A=3, K=1, nothing to phone home about!) on September 20th, 2020, mostly in the dark:
Here's 28 and 24MHz on June 5th a year later, with SFI=74-77, A=4, K=1, literally in the middle of the night (1:24am local time):
b) Solar flares and CMEs can degrade MF and lower HF propagation because they increase ionization in the D layer which absorbs lower frequencies.
I think it's important to distinguish between flares, CMEs and solar storms in this context. Flares affect mostly the day side of the planet, so MF is for the most part not much affected due to the D-layer preventing skywave propagation anyway. Flares can be responsible for rather short-term upper HF enhancements or the opposite - radio blackouts (depending on the flare severity) while CMEs cause slower, generally detrimental and more long-term interactions with the ionosphere and magnetosphere, up to solar storms. Unfortunately, my understanding of these interactions re HF and MF propagation is bad to non-existent.
This may happen even during the night when D layer is normally absent.
Not sure about what exactly happens at night. As experiments in solar eclipses have shown, the D-layer ionization drops significantly even within the few minutes of a total eclipse, where the moon shadow hits the ground. However, the ionosphere seems to respond with some sluggishness to X-rays, EUV and whatnot dramatically increasing the electron density in its layers, so it may extend into the night.
Related to that and probably with more impact, the season and propagation path must be considered in this regard - for example, in summer on the northern hemisphere, when the northpole is continuously facing the solar wind, over-the-pole paths and generally high latitude stations are permanently affected by anything coming from the sun, which can be felt even in the short nights. When there's much activity, the polar cap can absorb MF and HF.
I'm at 54°N in Europe (Germany) and during disturbed conditions I often observe a complete absence of shortwave signals from the US except maybe FL (most paths to the Northeast, Midwest or West Coast are over or too close to the pole and therefore dead) but the Carribean and South America keep booming in. This is also one of the reasons why summer is generally bad for transatlantic MW DX, particularly in a solar maximum.
1) Are there any other ways how solar storms cause propagation conditions to degrade? It seems to me that propagation may get worse even well above 10 MHz which should be less affected by the D layer.
If a solar flare (or more general SID) is strong enough to saturate the D-layer we get the famous radio blackouts, which AFAIK do not affect higher frequencies less or more than lower frequencies. However, on higher frequencies they cause noise on top of the absorption and DX stations on higher frequencies are typically more in multi-hop distance than those on lower frequencies, so these bands may
appear more affected.
Solar storms on the other hand are causing geomagnetic storms, which in turn cause ionospheric storms if I understood that right. They cause both degradation and enhancement or additional propagation modes like sporadic E or aurora reflection on VHF. The degradation consists of increased absorption and MUF decrease, that's why ionospheric storms affect the higher HF regions more (in their bad phases).
2) How do solar conditions affect longwave (LF) and VLF propagation? I have vaguely noticed that longwave stations may be stronger under conditions that result in poor HF propagation
The D-layer can refract frequencies below 250kHz, so any event causing more electrons in that layer could enhance LF? Other than that, I believe the geomagnetic field has a word in this too but like I said, I don't really understand the interaction.
Some not completely unreadable gobbledygook on the topic: