During your tenancy, your landlord or agent should provide you with contact details including a 24-hour contact for emergencies.
Increasingly managing repairs and maintenance is done online and communicating via email is a good way to keep track of progress. Whilst it is important to get repairs completed quickly, you should also be realistic about timescales. Some repairs may not be immediate, especially if replacement parts have to be ordered, but having a contractor attend within 24 hours to diagnose the problem is not an unreasonable expectation.
Most landlords and agents will hold a set of keys in order gain access to the property for repairs (it’s also useful if you lose your keys) but you should expect them to always confirm the access with you in advance before attending and give you the option to attend should you wish. If the contractor is attending alone, make sure that they are properly vetted and are insured to be able to collect keys and have unsupervised access
Property Managers are employed as agents for the landlord and, depending on the contract that they have with a landlord, they may be limited in what they can arrange without explicit consent from the owner. Although employed by the landlord they still have a duty of care to you as the tenant and to ensure that you are kept free from any danger. Most property managers will hold some money on account to cover the cost of emergency repairs but regular maintenance will need confirmation to proceed.
Emergency repairs are generally specific to power and water and most contractors that attend to these sort of problems (power failures, major leaks and flooding) will do the minimum overnight to stem the problem and then re-attend the next day when they will cause less disruption to other residents, be working in daylight and on normal rates.
If you have an emergency you should also take what reasonable precautions you can to prevent any damage, including switching off electric or water supplies or trying to contact your neighbour if there is a leak coming from their property.
Unless specifically agreed with the landlord and agent you should not try to undertake any repair works yourself, even if you are qualified to do so. Some works may potentially cause you harm, cause additional damage to the property or possibly invalidate the landlord’s insurance. If this happens the landlord could reasonably look to you to cover the cost of the damage if they did not give consent for work to be undertaken.