They should give samples of premium so people can test it.

My idea it that when people complete an achievement, they should get 3 days of diamond so people can see if they want premium. The free 3 days should not stack. Is this a bad idea?

nah most achievements are very easy.

oh

Free week if you sign up for their monthly or yearly sub.

Nah, "free" is when there is the button "Try fro free" without any additional moves including sharing my credit card data

All these are "additional moves" instead of normal "trial mode"

Well, that's quite comfy approach. I don't mind a few more clicks if it's a free premium. It's kinda like if a store had free items in it but you wouldn't consider them free cuz you had to go and get them instead of having them delivered right to your house.