Is there a way to restrict mines for certain ranks. Like, Rank A can visit Mine A. and Rank B can visit Mines A and B. But Rank A cannot visit Mine B

This is done using permissions - read the Rank Guidebook

The fact that so many people have the same question means that it's the software that's the problem. I propose a more developed system of ranks-mines integration in which:

• Mines can be added to each rank.
• Ranks inherit mines from previous ones down the ladder.
• Inbuilt mines protection: only ranks that are added to a mine can mine in them.

This ticket has been closed. If you have any other issues please open a new ticket.

mines.tp permission's already a thing and should works if you add it to the player on rankup command.
By default the /mines, the GUI will use the /mines tp command to teleport the user to the Mine.
This can be edited from the configs (check all the Config.yml, GuiConfig.yml and autofeatures).
This feature's still confusing and could become the only and recommended way to TP to a mine supported by Prison to achieve the AIO definitive plugin feature.