Fiddle-leafed Figs are quite pest resistant. Where did you see the webs? On new leaves just emerging or older leaves?
The leaf spots are caused by lack of light and letting the soil get too dry. You cannot give this plant too much direct sun when indoors, so move it right in front of and close to your sunniest window.
Likewise, if it is still in its original nursery pot, then it is pretty hard to over water. Water it thoroughly as soon as the surface of the soil feels almost dry, but not completely dry.
Unfortunately, the damaged leaves will always have those spots unless you trim them off. However, with better light and watering, new growth leaves should be fine.
Skip the fertilizer spikes. You can use any liquid fertilizer at half strength but no more than once per month. I also suggest you stop using neem unless you have identified a specific pest.