1) What is long-term accommodation like? I know I should just show up there and look around, but if anyone has any details about places, rates etc...
There's a bunch of decent long-term accommodation on Koh Tao - but finding it tends to rely on 'word-of-mouth'. It's typical to arrive and seek economy (pay-per-week) accommodation for the short-term, whilst networking to find more efficient long-term options.
On arrival, you might want to look at the rooms available in Mae Haad (where the pier is), as these are cheaper than the resorts in beach locations. The top of Mae Haad hill (the two roads that run up there) is a good place to start. Most of the long-termers stay in cottages that are set-back, away from the beaches in the hills.
The prices are much better further from the beaches - but you might want to budget for a scooter for transport. There's usually plenty of scooters being sold cheap (renting long-term is expensive)... again, networking to find those... there's always someone leaving who needs to sell-up (same for furniture etc). You'll also want some transport for going shopping - the better supermarkets (not tourist prices) aren't located near the beach areas. Same is true for monsoon season - you won't want to walk anywhere far during the heavy rains. Also, if working as a freelancer (common when you first get there), you'll need to transport yourself, and all your dive gear, at short-notice to different dive centers - a scooter can be critical for that.
Here's my old house - affordable to a 'regular' instructor or working-couple. Located about 2km back from the beach. 1 bedroom, kitchen, lounge, reception, furnished with cable tv.
2) How realistic is it to walk places? For reference, I am a long-distance runner, so I have a relatively high tolerance for how far I'm willing to walk to places.
It's easy to walk between Sairee and Mae Haad. The other bays/locations aren't accessible on foot on a day-to-day basis.
3) What is the deal with keeping my belongings safe? My dive gear will mostly be with me during the day, obviously, but I also will have a Macbook Pro and a Canon DSLR. Are there safes at most accommodations, or is that not even an issue?
There were spates of 'break-ins' when I was there. I used to take my laptop into work with me each day - it was safer locked/supervised in the dive center, than left at home, when I was out diving. I never heard of a house having a safe, although that wouldn't be a bad idea, if you could arrange it.
4) Any suggestions for what I should pack? My dive gear, bathing suits, sunscreen... that is clear. I am looking for the not as obvious things, that I would not necessarily think of.
Clothes, holiday 'stuff' (sunscreen etc) dive equipment are readily available on Koh Tao. Same for music, DVDs and other entertainment stuff. Luxury/expensive items are rare - take those with you (or buy them in Bangkok on the way).
Check that your scuba equipment can be serviced there - I went with Poseidon regs for my tech kit and ended up selling them, as spares weren't readily available.
Consider taking a 'spare' credit card, or something like a Travelex card. Many of the banks will occasionally flag up a 'warning' about suspicious spending because you are in Asia long-term. I've had a bunch of credit cards blocked/frozen for no good reason - and that can cause some significant money issues. I got a 'Travelex - Cash Passport' because it won't get cancelled and I can transfer money to it via online banking - which means I always have access to my money, even if my credit card gets frozen.
Scan all your important documents and email them to yourself - that way you can retrieve/print them anytime you like, at any internet cafe.
Same for all your important phone numbers; friends, family, embassy, local consulate, DAN, bank, credit card etc. Put them all in an email and send them to yourself, so that they are instantly accessible in an emergency.
On arrival, investigate all the critical local points-of-contact - your embassy/consulate, 24hr medical/accident clinics, recompression chamber, police etc. These are typically hard to find at short notice, via word-of-mouth etc. Put them on your phone (local sim card) and stored via email. I was amazed at how many 'resident' divers didn't have immediate knowledge of this stuff... and then panicked at 2am when they saw someone crash a scooter etc.
5) Anything else I should know about the place?
If you're not prudent with your funds, you'll go home a lot sooner than you plan for.