Lady at Immigration is correct, there is no 90 days Extension of Stay, you can only apply for the 60 day Extension of Stay based on visiting family or the 1 year Extension of Stay by meeting the requirements.
The can apply for a 30 day Extension of Stay based on tourism.
an adult cousin can not get any visa based on you working in Thailand.
Your mother could get the Non Immigrant O visa based on a foreigner with a long stay, but that also needs documentation of your employer, talk to them for further information.
You can check in and pass immigration on the airport before 23:59 hours.
If you go later a stamp for overstay will be placed in your passport.
First day is most of the time waved for fines but if you have two days all days are fined with 500 thb a day.
You can apply at Immigration for a new Extension of Stay and if you can not meet requirements you get a stamp Application not approved and 7 days to leave the country, cost of this application is 1.900 Thb.
No problem, it is known that a stay from a tourist visa can be extended once with 30 days and if needed a booking of a train ticket to a foreign country counts as onward travel.
You can apply for a Single Entry Tourist Visa which gives you 60 days of stay, than go to Malaysia as planned, come back into Thailand without a visa and get 30 days Visa Exempt Entry, which can be extended once with another 30 days.