My sylestie has reached 60. Is that the highest a sylestie can reach? If so, can they still get proficiency points? How or when do they get more? Also, is the diamond shop the only way to get a genetic testing kit? It's called the exceptional kit, is there a lesser kit, or a greater kit?

Level 60 is currently the level cap with proficiency points capping out at 12 , however the level cap will increase to 75 with proficiency points capping out at 15 with the release of the MegaZone.

The diamond shop is the only way to get an exceptional genetic testing kit (best to get them while they're on sale for 1000 diamonds) however there may be some lesser testing kits floating around somewhere on some players account. For the moment you can always request testing from another player in this forum until you can buy your own.

In regards to obtaining diamonds, if you can't buy them with RL currency, you can always by diamonds from your fellow players via the currency exchange with sylestia gold.