There is a thin pipe coming from wall on the left that attaches to this metal filterlike coil thing. This coil thing is this very dirty, is it a filter? The dirty filter thing measures 1.5" thick, 8.5" deep and 34" wide from pipe entry to end of white metal cabinet that its encased by. Building said they use oil/natural gas for heat so not sure what type of radiator this is? I wanted to build a nice wooden window seat to go over it, can I do this with this type?
It appears to be a "forced hot water" radiator, unless there is a steam vent you're not showing us. Also called "fin-tube radiators". How the water is heated is not entirely relevant (oil, gas, wood, coal, electric, solar -- same radiator). The fins conduct heat from the water in the supply pipes (tubes) and "amplify" the transfer to the air, which flows across the fins. Airflow may be natural convection or mechanically forced by a fan.
You need to straighten the fins for best airflow (there are heavy-duty "combs" made for the purpose) and blow/vacuum them out from time to time, if you want to maintain maximum efficiency. You can dress it in wood if you like. They are generally designed to carry water no hotter than about 180 degrees F. Wood will not be as good at conducting or radiating heat as the metal enclosure. You must provide adequate air vents in any enclosure so that the warm air has a way to heat the room.
My fin-tube baseboards run nicely at around 150, except on the coldest days, at which point our on-site engineer raises the boiler temperature and chucks in more wood.
That type of heating unit is called a convector and was probably made by "The Burnham Boiler Company". It was designed to utilize low pressure steam (15 PSIG) or hot water as the heating medium. Your is probably hot water since the connection piping looks like that of a hot water system. Changing the cover design will affect the heating output of the unit. Almost any type of wood product can be used. Cleaning this heating unit can be done with compressed air, vacuum cleaner or a water hose is the installation allows. The fins should be straightened if possible with a fin comb. The fins are usually aluminum or they could be steel if the convector is old enough. The fins shown are aluminum. If you decide to try and straighten the fins use protective gloves since the fins are thin, sharp and will cut you. Building a window seat above this unit will reduce the heat output so be careful of what you build, and how restrictive of the air flow you make it.
It's not actually a filter, it's a radiator. The fins radiate heat.
It's best not to cover it in wood, you might be surprised how hot that thing can get. Covering it may require some intense Pinterest research. ;)