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This article should help: https://www.gardeningknowhow.com/plant-problems/pests/insects/spittlebug-control.htm

Mulching does help when growing strawberries, and straw is preferable. These articles should help: https://www.gardeningknowhow.com/edible/fruits/strawberry/growing-strawberry-plants.htm
https://www.gardeningknowhow.com/edible/fruits/strawberry/sweet-strawberries.htm

If the leaves are nice and healthy, I would leave them alone. The leaves are the food-manufacturing parts of the plant, and care should be taken not to remove these functional leaves. It could also open up the plant to pests or disease. If you have older or browning leaves, these can be removed without any harm to the plant. You can always move the leaves around some to allow for more light but the plant will still produce just fine as it is.

Your strawberries can be cut back in late autumn.

The plants depleted the phosphorus in the soil, which helps with flowering and fruiting. Bone meal is a good organic ammendment to fix this. You can also use a high phosphorus fertilizer (typically sold as a "bloom booster" fertilizer).

Other than allowing the plants to dry out some now, there's little else you can do. In the future, NEVER store any plant in water as this will lead to rot and the ultimate loss of your plant. If you are worried about potential drying of the plant, you can water it occasionally to prevent this.