Your coinsurance or copays count toward your annual out of pocket maximum. Note that only the procedures covered and approved by your insurance count toward the out of pocket (so if you pay for something that they denied or wasn't filed with them, it won't count).
FMLA generally covers employees if you've worked a minimum number of hours (I think its 1,200) and if the employer has over a certain number of employees. It is only job status protection for up to 12 weeks of leave and does not provide any pay. Individual states in the US sometimes have higher requirements, and some employers offer more than FMLA as part of their benefit packages. I am currently on FMLA which means my employer can't sack me or demote me just because I'm off work for medical reasons. I also have short term disability paying me my normal salary for up to 11 weeks, then 85% for another 12 weeks (if I need it). I believe my employer is above average for benefits compared to other US companies.
With COBRA - you get to continue your health insurance after terminating employment, but you pay the full premium vs getting your employer's contribution toward the cost. Continuity of coverage and no preexisting condition can be a big factor, but it may be expensive - you might be able to find out how much it would be (my company's HR office provides a statement each year letting us know how much they paid toward these types of benefits).
I'm sure availability varies according to location, but it took me 13 weeks just to get an appointment with a neurologist once my GP and I decided my symptoms indicated a referral was needed - they were booking 17 weeks out and I took a cancellation. Add another 4 weeks to get some lab work done, and an MRI authorized and scheduled. If that's the kind of timeline you're looking at, it may factor into your employment decisions.
Also, if you have an AN, surgery is not necessarily going to have a horrible impact. I had a large (3.1 cm so too big for radiation treatments) tumor removed translab last month, and presently my main concern is my left eye doesn't make tears - its a bigger pain than I thought it would be, but that started happening before the surgery. I'm still resting up, but I have not had a worsening of senses or nerve function, I'm just hoping to reverse what happened in the 6 months prior to surgery. From what I have gathered here and from my neurosurgeons, both radiation and neurosurgery have advanced in recent years - I say this so you won't worry unduly if you are diagnosed with a tumor. Frankly, I was concerned my symptoms might be Lyme disease or MS. I'd take an acoustic neuroma or quite a few forms of cancer over MS if I had a choice.
You would do very well to ask about benefits, options, costs, and so on - call your insurance company and ask them to explain your EOB. I know quite a lot about these things, and yet likely call and ask for explanations more than most because I'm not shy and feel it is their duty to help me if I don't understand their communications. I've uncovered quite a few mistakes along the way so don't be afraid to ask - you'll need to know this stuff some day, even if you find out there's no tumor after all.
Good luck!