When is it obligatory to say "Bismillah" (in the name of Allah) before eating during the day? And is it repeated when drinking tea after lunch if there is a time interval? And is it necessary to remind others to say "Bismillah" despite their annoyance?

There is no specific number of times one should say "Bismillah" (in the name of Allah) per day. Rather, it depends on what a person eats or drinks. Whenever a Muslim intends to eat or drink, even if it is just a cup of water, it is legislated for him to mention the name of Allah the Almighty. He should renew the "Bismillah" for each new item he consumes. It is also commendable to alert others to this Sunnah, either directly or by pronouncing "Bismillah" audibly for them to hear.