I would recommend Melatonin over Valerian root. The reason you don't sleep during the daytime is hormonal. Hormones are entrained by light/dark cycles, meal patterns, and exercise. Melatonin is the hormone your body produces to make you tired and to go to sleep. When you're exposed to high-energy visible light (blue is the primary culprit, followed by green) your body does not produce melatonin. When that light goes away, your body starts producing it again.

However, just blacking out your room is not usually enough to make you sleep during the day because of the natural entrainment of sleep patterns; Your body produces melatonin not just when it's dark, but when it is used to going to sleep. Melatonin supplements basically let you circumvent that whole problem because you don't have to wait for your body to produce the melatonin. Once your'e asleep, your body's natural systems take over, continuing to produce melatonin, regulating your sleep-stages, and basically allowing you to sleep normally.

Valerian root is a GABA-ergic compound (specifically, a GABA-a receptor agonist, like benzodiazepines, ambien, and alcohol) which means it does not function on your melatonin pathways, it's a sedative. Alcohol and Benzos are well-known to disrupt your sleep cycles and to favor deep sleep over REM sleep which makes it less restful and can lead to dependence. You can also end up with a glutamate-rebound effect that wakes you up when your body overcorrects after the valerian wears off. Basically, you should think of Valerian as a GABA-ergic sedative/hypnotic drug like Benzos (xanax, ativan, valium, etc.) or alcohol, not as a supplement. Just because it doesn't require a prescription does not mean it is not a drug.

If you can't tell, I'm not a fan of Valerian. I'm personally pretty sensitive to excitatory rebound effects, but I definitely got them from Valerian. I would definitely recommend staying away from that stuff.

Regarding your other points:

First of all, as a vegan, you're at risk for a lot of deficiencies. Why are you a vegan in the first place? If it's just for health reasons, I would highly recommend switching to ovo-lacto vegetarian and/or including fish. Both groups have demonstrated significantly higher longevity than vegans in epidemiological studies. Either way though, you might want to look into Cronometer. It tracks the vitamins and micronutrients in your food. If you track everything you eat for a week but try not to let it influence your food choices, then at the end of the week, you can pull a report and see where you averaged out in both micro and macronutrients. That can be a good way of identifying deficiency risks. You can then address those either through dietary interventions or supplements, the former being preferable of course.

1. Probably a good idea, but check cronometer to see where you currently stand
2. Never heard of it before this, but looked it up and it seems like a decent alternative. Ideally, make sure it's independently lab-tested for toxins and make sure it doesn't have too much Omega-6 (n-6) in it or it defeats the whole point of supplementing n-3 (improving your n-6:n-3 ratio). Something I've noticed with Vegans is that they tend not to be careful about the types of fats they eat since they're so restricted already. Think about the purpose you want the Algae oil to fulfill and check if there are any other dietary modifications you can make to assist with that, like cutting out sources of omega-6 polyunsaturated fats. Remember: Saturated Fats and Monounsaturated Fats are healthy. Polyunsaturates (vegetable oil and seed oil) are bad.
3. Probably only reasonable if you are deficient. There is zero evidence that multivitamins improve health otherwise, and epidemiological studies have shown a positive correlation between multivitamin intake and all-cause mortality.
4. Beans are not a complete protein, meaning it is missing certain essential amino acids. If you don't have complete proteins, or at least a complementary incomplete protein that make up for the specific EAAs you're missing in the beans, you'll become deficient. Definitely use the Whey (great, easily-digestible, complete protein) if you can. Get a tasty chocolate one and blend it with coconut milk, water (for consistency), bananas, and ice. Throw in some nut butter if you want. I'd say this is one of the more important recommendations here. Alternatively, grab a vanilla one (I like Optimum Nutrition's Vanilla Creme for this) and mix with orange juice or blend with OJ, Bananas, and Berries. It's very easy to make it taste good and totally worth it.

Let me know if I can help clarify anything or if you have any questions. Cheers