You should call an electrician when you start losing power to devices, lights flicker, or if you smell any kind of burning smell that follows with a crackling or popping noise. Also if you need to do any electrical work always leave it to the professionals.
You will need a new electrical circuit if your adding anything new in your house to prevent overloading of circuits. Usually a microwave, fridge or any appliance will require a dedicated circuit.
To fix an overloading circuit it's always best to split whatever is on that circuit and make sure you follow the nec code on which circuits need to be dedicated and which circuits can share with other circuits like outlets, lights etc.
Yes we do this all the time and dimmers work great with most LED applications.
If the outlet is hot to the touch, or the prongs on the plug don't hold in the outlet, or if your outlet is more than 10 years old I would recommend changing or at least having them inspected for quality.
No you should never use power strips unless they have a built in surge protector, extension cords and power strips are major fire hazards and should be not used except when temporary.
Your circuit breakers will feel hot if they are being overloaded or when they lose their integrity and get old. You should have an electrician inspect your panel semi annually or once a year to be safe.