Can I transfer my lease to another complex within the same company?

If you want to rent a different apartment in another apartment complex, it would be subject to a new lease.  Your current lease is only for your present apartment.

As for the plumbing problems in your current apartment, in every lease there is an implied warranty of habitability which requires the landlord to maintain the premises in a habitable condition by complying with state and local housing codes.  When there is a breach of the implied warranty of habitability such as the plumbing problems with the water leak, the tenant notifies the landlord as you have done, and the landlord is required to respond within a reasonable time by making the necessary repairs.  When the landlord fails to respond within a reasonable time, the tenant has the following remedies:  The tenant can make the repairs (call a plumber) and deduct the cost from the rent or the tenant can move out and terminate the obligation to pay rent for the balance of the term of the lease or if the tenant remains on the premises, the tenant can withhold rent and defend against eviction.  Another alternative is to sue the landlord for breach of the implied warranty of habitability.  You can also contact the local housing code inspector, who can bring an enforcement action against the landlord for housing code violations.

You did not mention what other problems in the apartment you are having, but NOT all maintenance problems rise to the level of a breach of the implied warranty of habitability.

You do not have a right to transfer your lease, though certainly the company could agree to let you do this. On the other hand, all rentals come with the "implied warranty of habitability," which obligates the landlord to provide rental premises which are "fit for their intended purpose." Significant water problems--not having water, for example, or no hot water in a residence or business which needs  it; large leaks which lead to mold or cause certain rooms to not be usuable--can violate this warranty. If the warranty is violated, the tenant could potentially do one or more of the following: treat the lease as terminated and leave; sue for compensation (a rent credit) for the time the premises were affected; seek a court order compelling repairs; pay for the repairs, then deduct the cost from rent. Before doing any of this, consult with a landlord-tenant attorney; if you try to do this but it turns out the situation is not severe enough to constitute a violation of the implied warranty of habitability, you may end up in breach of your lease.