QHow do I discard a random card?

AFor example, if you have 6 cards, you could assign each card a number from 1 to 6 and then roll a 6-sided die. If you have 3, you could assign two numbers to each card and then roll. If you have two, you could assign three numbers or flip a coin. Alternatively, you could shuffle your hand and simply have someone else pick a card.

QIf I have 2 copies of this follower on my field, do spells my opponent plays cost 2 more?

AYes, they do.

QIf this follower is on my field when my opponent banishes 10 spells in their cemetery to play Dimension Shift for 7 play points, do they have to pay 8 play points instead?

AYes. Effects that change the cost of playing a card to a specific value are applied before effects that increase or decrease that cost.

QIf this follower is on my field when my opponent plays a spell for 0 play points with Merlin's On Evolve ability, does it cost 1 more?

AYes. Your opponent must pay 1 play point to play the spell. If they can't, nothing happens.