A subconjunctival hemorrhage usually appears as a sudden, spontaneous, bright red patch on the surface of the eye. This occurs when a small blood vessel breaks in the lining over the eye (the conjunctiva). It is usually otherwise painless, and the vision is not affected. The redness can be quite dramatic. This can occur spontaneously, or after direct trauma, sneezing or coughing, or straining. It often happens overnight while sleeping. High blood pressure is another possible cause. The redness usually disappears over a one week period. While blood thinners do no typically cause this condition, it may make it appear worse. There are rare cases of clotting disorders that can also lead to this condition. In some cases the hemorrhage can stretch the conjunctiva which can cause pain. In these cases, the conjunctiva might be swollen or raised, and could lead to patches of dryness on the cornea due to a disturbance in the tear flow that lubricates the eye.
You are exactly right in your thinking. Different drops are used to dilate eyes. Tropicamide (mydriacyl) is the most common drop and it comes in two strengths, % and %. The % will not last quite as long but it is not a large difference. Tropicamide will dilate the eyes and interfere with near focusing. Phenylephrine is often added as a second drop with mydriacyl to enhance the dilation. Phenylephrine enlarges and hastens the dilation but has no effect on focusing and usually does not prolong the dilation. Paremyd is another drop containing % hydroxyamphetamine and % tropicamide. It does not dilate the eyes as well but tends to last a shorter time period and not interfere with near focusing as much. Longer lasting drops include cyclopentolate and homatropine. They have a longer mode of action and exert significantly more interference with close vision. They are usually used for children.