or tailor each CV to fit the school and then email it?
But don't bother tailoring it too much or making it too detailed - they get a lot of CVs, most of them too lengthy to read, most of them irrelevant. It should say what you want (lessons), why you can do it (Celta) and who you are (an EU citizen) - they can figure out the rest. As important as the CV (or more so, sometimes) is a schedule of when you're available for lessons. If you aren't doing many, fill in a few spaces in your timetable to look busier, making clear they are flexible and changeable and that you're happy to do cover classes without notice.
Should I walk into every school and hand in my CV (which I really hate doing!)
No. You'll probably only see the receptionist or some bod that doesn't hire or fire. But when you mail a CV. say you'd really like to call in sometime for a chat - they will remember you.
What hours should I be expecting to work and what is the average starting salary?
Bookends. Meaning in-company lessons at the start of the working day and open groups in the early evening. This is normal, though there are exceptions. For example I never did open groups, except when someone was away. In Warsaw, as a new teacher without experience you should get about 40zl per 45 mins, more if you're over about 35 and less if you're very young or non-native. If they contact you at short notice, haggle upwards, othereise don't bother. Krakow has an oversupply of teachers and the EFL market in PL is declining. Called in the industry 'the Venice effect'. At least by me.
Any schools I should watch out for
At risk of a chorus of approbrium, I'd say the ones owned by British people tend to be better and the ones owned by Poles tend to be worse. Though there are certainly exceptions.
I notice a lot of people on these boards saying there is more money in proofreading, copy editing etc. How does one get into this area?
With difficulty. Contacts though colleagues or (the right sort of) in-company clients usually.
I am good at English and I actually know the difference between there, their and they're so I'm figuring I'm already a little ahead of some native speakers
But not necessarily ahead of the ones who are teaching English, who have (or should have) the difference between a defining and a non-defining relative clause at their fingertips, and most importantly, know how to teach it. But don't be disheartened - the most important thing is how good you are at making sure your students learn. All the rest is incidental.
Would really appreciate any advice. I don't want to be one of the unfortunate few who has to leave this beautiful city :(
Don't give up. Keep on sending your CV. They throw them away/delete them and generally find they need a new teacher at awkward times. If they've met you, even once, they'll remember you. Keep going. A foot in the door, however mall, makes you feel better and invariably leads to more work.