Big grey cylinder is a sand filter with a multi-purpose valve (MPV) on the top.
No heater. No chlorinator.
The light blocks seeing where the three pipes from the pool go to. At least one pipe is the suction water from the pool into the front of the pump. The water exits the pump on top and is pushed into the filter MPV. The water flows through the sand filter and back to the pool returns.
The first pipe, most right most, is a waste line from the MPV that discards dirty water when the filter is backwashed.
The plastic buckets are chemicals that TFP probably does not recommend using.
Labor is the biggest part of any pool reno. If you know how to DIY, and there are no shell or plumbing cracks/leaks, you should be good to go with an estimate close to Allen's.
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