The lease survives the sale and the new owner must honor it. Unless there is a special clause in the lease giving the landlord the right to terminate in case of sale.
When you purchase a property with existing tenants, you may have to honor the lease but I would definitely check the lease agreement.
Yes. When a buyer buys a property with an existing lease, your lease is valid until the expiration date. Then it is up to the new owner to either renew your lease with or without an increasing your rent OR not renew your lease at all. The new owner must give you a specific number of days by state law to notify you before your lease expires.
You can purchase property as per the Transfer of Ownership Act,
Transfer of Property Act, 1882
55. Rights and liabilities of buyer and seller
In the absence of a contract to the contrary, the buyer and the seller of immovable property respectively are subject to the liabilities, and have the rights, mentioned in the rules next following or such of them as are applicable to the property sold: