That means they made a mistake. It happens all the time. It's your responsibility to check your stamp in your passport every single time you get a new stamp. Immigration officers are humans and they make mistakes. You'll likely need to go back to where you got your stamp to get it fixed. Or just do a border bounce to leave the country and return again, this time making sure you also give them your printed out visa if it's an e-visa and making sure you get the correct stamp upon entering again.
Is it okay? That's up to you to decide. The legal requirement is that YOU have the money in your bank account for a certain number of months. By using an agent you are basically skirting the law through bribery. So whether it's okay or not is up to you decide.
Laos has still not announced when they will switch to e-visa. But you need an appointment at both of the embassies in Laos and they're often booked up for a few weeks.
Taipei is a good option. They're on e-visa but they issue the DTV the same day you apply normally.
If you don't enter Thailand before the end date on the visa, then your visa is expired and it cannot be used and it cannot be extended. You would need to apply for a new visa from the embassy.
Only ever asked for if they are looking for a reason to deny you entry. If you don't have any past issues with Thailand, then it should not be asked for.
You can do it after 90 days, and maybe even again after that. But know that once you've been in Thailand for about 180 days, you will likely face problems trying to enter again if you don't have a proper long-term visa. You cannot live in Thailand on short term tourist stays, and eventually you will be pulled out of line and questioned about what you think you are doing, and possibly even denied entry. No one can tell you if or when that will happen as each entry is up to the individual immigration officer you are standing in front of.