the 2 times by land per annum no longer applies. Land entries are now treated in the same way as air entries but be aware they are cracking down on this behaviour
you can apply for a Non-O visa based on having money in a bank outside Thailand if you apply outside Thailand but to get a 12 month extension of stay you need funds in a Thai bank for 2 months before applying for that extension
I don't use that immigration office but my one definitely do check. This year I started doing 90 day reports online and have had 2 visits 6 months apart
Normal bank statements from your bank should be used, if they are not in English or Thai you may need to get them officially translated. You don't say where you are applying but different embassies have differing requirements as to how long the 500k must be in your account, some only require it on the most recent statement, some require it on the date of application, some require it to be in the account for 3 months or more