Either... whether I know I can say "it's either this or that", but is "it's whether this or that" correct too? Same question for "whether/either you like it or not..." thanks for your help

Where I live : Tahiti, French Polynesia Tahiti is an island in French Polynesia. French Polynesia is a group of islands that is an overseas country attached to France (so we're all French here). It is located in the Pacific Ocean, between New Zealand and Hawaii. A lot of tourists come here for their honeymoon or to feel at peace, closer to nature. They usually come to Tahiti, and then visit Bora Bora and Moorea, they're like islands that you have to visit if you come here (if you're crossing an ocean, might as well go to other islands and enjoy as much as you can...!). In the past, there were a lot of asians who came here to seek a better future and left their home town. That's why nowadays there are a lot of mixed people here. There are still full Tahitians, mixed people from Tahitians and Asians from South East Asia, and French people (Tahiti was colonized by the French in the 1900s). This was a short introduction of my home town, feel free to correct me if I made any mistakes ^^

Is "there is + plural" correct? I hear a lot of english native speakers say and write things like "there's a lot of days/times/problems/answers...", shouldn't it be "there are a lot of..."? Or is there an exception or something like that? thank you in advance !