Hello from JustAnswer.
For most birth control pills, taking the ill within a couple hours of the same time each day will make it effective and you would be protected from pregnancy during the encounter last night. The mini pills, which only contain one hormone, is more sensitive to the time that it is taken, but most birth control pills that are used are combination birth control pills, and there is a greater tolerance to when you take it each day.
It is important to note that multiple studies that look at people remembering to take pills show that taking it at a consistent time each day helps to build it into a habitual pattern, so that it is less likely to be forgotten, and this as true for birth control pills as for blood pressure pills. So, many doctors will emphasize taking the birth control pill at the same time each day, because that is the best method to assure that you do not accidentally forget to take a pill each day, and forgetting the pill for the day has a significant impact on the effectiveness of the pill.
However, in your case with taking the pill within 2-3 hours each day, the birth control pills will maintain their effectiveness and you are protected from the encounter last night.
Of course, protection in this context only means protection against pregnancy. The birth control pills do not provide any protection against STIs, so depending upon the commitment of this relationship, there may be other reasons for the use of condoms.
Yes, it is fine to simply toss the placebo pills. They are only there to maintain the habitual taking of the pill each day. Some of the pills add iron to the placebo pills, so that there is some value to swallowing them, but from the perspective of protection from pregnancy, there is no need to swallow them, and tossing them is fine.
If I can provide any additional information, please let me know.