idk about immigration checking wp status but at some point they'll find out. Again, it does not matter what date you are stamped into the country till. This is a big mistake many people make. Wp ends, reason for extension ends, you MUST report to immigration immediately. You can do this one week earlier too. Doesn't have to be on the exact date.
This was my exact experience last year. Robert above is a moderator so follow his advice. Just want to add... Who told you you can stay till the 23rd? Your employer? Don't believe them... Only believe immigration. When you go cancel your extension of stay, you can apply for a 7 day extension denied" stamp to get your stuff in order and then leave. But if you are planning to come back here for two or three months anyway, just leave and go to Vientiane (or another consulate abroad) to apply for a single entry tourist visa which gives you 60 days plus 30 day extension. Good luck.
Live and work in Bangkok on a non-B visa. No need for TM-30 (for now!) and if you work for a company/school, they often have someone who can do 90 day reports for you.
You have a visa exempt stamp not a visa. You cannot get a re-entry permit when you enter visa exempt. Just fly in again, and get another stamp. To be safe carry proof of accomodation, ticket out of Thailand and 20,000 baht cash.
The Swiss embassy in Bern clearly says you don't need a visa for tourism purpose (first line), but that "Swiss Travel Document" sentence is confusing. A "reiseausweis" is not a passport though so it doesn't apply to you as a Swiss citizen. As for your other questions, Tod answered them.