that thing is in dire need of a full suspension service. Rear shock probably has no gas left in it, and the oil probably looks like mud. The front forks also probably look like mud in addition to losing oil through the seals. Around here you can get both serviced for about $500 total.
No need for an inline filter. Im not sure about the sputtering but you could try removing the pump and cleaning the pickup. Personally i'd start with all the basic maintenance items like plugs, valve adjustment, air filter, suspension service.