What is a tenant’s right to break a lease early?

Sorry to hear about your brother.

If the tenant moves out without the required notice, the tenant remains liable for the rent for the balance of the term of the lease or until the place is re-rented whichever occurs first.  The landlord has to mitigate (minimize) damages by making reasonable efforts to attract new tenants.  The landlord cannot just allow the place to remain vacant for the balance of the term of your lease.  Reasonable efforts on the part of the landlord to find another tenant would depend upon what other landlords in the area are doing to attract tenants; for example, posting a sign on the property advertising the vacancy, advertising in the newspaper or a local rental guide, etc.

Since you have found eligible tenants, when they rent the place, your obligation to pay rent ends. However, if they are paying less rent than you were paying, you would remain liable for the difference in rent for the balance of the term of your lease.  The landlord has to have a valid reason for charging the new tenants a lower rent such as market conditions.  If the landlord does not have a valid reason, the landlord has failed to mitigate damages and the landlord's damages will be reduced accordingly in a lawsuit against you.

As for your security deposit, you should be able to recover the security deposit when the place is re-rented. The landlord should provide an accounting of deductions from the security deposit such as for cleaning or repairs, etc.  You can sue in Small Claims Court regarding the security deposit.

As for the landlord showing up without notice during your tenancy, notice is required in order for the landlord to enter your rental unless it is an emergency. In a non-emergency situation, the landlord is required to give notice prior to entry and the entry has to occur during normal business hours.  The amount of notice varies from state to state.