How is your fish doing?
If youaren't feeding him regularly by now, I would start again. The pea is just fiber to help clean out his gut, just like the daphnia, thats why they are recommended. But Bettas are strict carnivores and he's not getting anything from that pea. So don't forget to feed him.
And though I hesitate to change a system thats worked so well for your Betta... in his older age, he may need more frequent feedings. You can make them even smaller... but a Betta should be eating at least every day without fail. Once a week they can have a break and have the pea to clear out their system... but I wouldn't leave them on one of those eating every other or every couple days schedule.... it's not healthy for them. In the wild they eat tiny creatures whenever they happen upon them.
I wouldn't change too much in the tank... try to think any changes out carefully before you take them, when your fish is already ill or delicate. If there might be an enviromental cause for the oily surface, find it and fix it... but keep him in the same home hes used to because a change is stressful. If you can only get a little airstone or bubble something... just get one of those. They do not filter, no.... but they do make it easier for an ailing fish to breathe by enabling them to use their gills as well... the extra oxygen can decrease populations of harmful bacteria and increase the good bacteria.... and I found my fishie who had a bit of fin rot just recently... loved to sit right over his bubble wand... and he got better so much faster... I think he was taking a "bath" in bubbles, and it helped "wash" the bacteria off him.
Remember that bacteria and illness, especially in the case of an old or a stressed fish... is not always your fault or the result of dirty water. The bacteria that cause fish illness are *always* present in their water, from hands/equipment, from the air itself in the room contacting the water, their own bodies even shed it from previous enviroments. Whether they get sick from it or not has to do with bacteria count (lack of cleanliness), other fishie stressing factors, and their general health & immune system.