A tenant is required to fix or repair any item they damage as part of their duties as a tenant. The landlord is required to keep the premises in habitable condition. So, if the leak under the sink was caused by the tenant, then yes, the landlord could ask the tenant to pick up the cost of the repairs. You'll want to check your rental agreement carefully as most commercial agreements contain provisions which would prohibit a tenant from undertaking a plumbing repair (although not normally phrased in that fashion) You'll want to contact an attorney who is familiar with landlord tenant law (don't go to a law firm that does these occasionally) and get an opinion based upon all facts and a reading of your rental agreement.
A proper response would require a thorough investigation into the history and background of this relationship. The information provided above is just that, information, to be used as you see fit.
It depends. As Mr. Fitch mentioned, if you caused the damage, then you are liable to repair it. If you didn't or the cause cannot be determined, then you must look to your rental contract. You should consult with a landlord tenant lawyer in your area for a thorough review of the facts and the rental agreement.
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