The question is to choose between each of the options

Incineration/landfill
The answer is totally dependent on what is being disposed of. For the purpose of this exercise let’s assume the disposal of mixed waste with no materials recovery.

Incineration is the best option as the process can deal with most of the issues surrounding disposal of mixed waste. The volume of residue for landfilling is about 10% by weight of the original input and there is the possibility of energy recovery.

Landfilling mixed waste results in decomposition over a long period of time with the danger of leaching of toxic liquids into ground waters and the production and release of methane gas into the atmosphere.  Modern landfills do have processes to minimise these problems but they remain an issue over very long periods of time.

The real solution is Mechanical Biological Treatment (MBT)  followed by gasification. Where recyclables are removed from the waste the biomass content is either composted or processed through Anaerobic Digestion (AD). The remaining residues can then be further used for energy recovery by a process of pyrolysis/gasification. These processes create almost no emissions, other than those created by using the gas generated for energy, which is similar or lower than natural gas. The final residues are inert and can be safely landfilled.

Hot Air/Paper Towel
I would go for Hot Air drying on the assumption that a hand dryer has a reasonable lifespan with the original environmental cost of production spread over this time. The only other EI is the energy used to generate the hot air. Paper towels on the other hand use large amounts of energy and water in their production and even if they are recycled and returned for manufacture, the water and energy needs for producing even cheap paper is substantial.

Of course with a little patience, ones hands will dry naturally in a couple of minutes

Dish washer/hand wash
A dishwasher is basically a robot and it is claimed that they use less water for the amount of dishes washed than hand washing.  Having said that, coming from a time when there were no dishwashers, they do create bad habits and encourage people to wash their dishes a lot more.  As well as this, in order to make best use of the dishwasher, they need to be full. This means having a lot more dishes and cutlery available, which have to be produced with all the environmental impact of their production.

If we have to wash everything by hand we will use one knife to butter all the bread, one spoon to sugar all the teas, and the breadcrumbs from plates that have sandwiches on them will generally be wiped with a dry cloth.

So, for the environment, hand washing is the way to go, for me and convenience, I still use the dishwasher.