Texting: Download WhatsApp to your handphone for free SMS texting. With 800 million users it's likely your contacts are already using the app.
Taxi: I didn't take taxis in Los Angeles so I can only compare this app to uber. GrabTaxi works a bit like uber in the sense that you input your location and destination, book a taxi, see its ETA. For every ride I have booked I have paid cash as requested in the app, but you do have the option to pay with NETs. You will receive promotions via email for discounts on future rides that must be used within a time period.
Food: Instead of Yelp, hungrygowhere.com is much more widely used in Singapore. Whereas Yelp is strictly about user-generated content and reviews, HGW is more like a blog with articles, promotions, and a lot of "top 5"or "top 10" lists, but just like Yelp you can read restaurant and hawker center reviews, search by location, type of food, price range.
MRT: SG MRT (map of MRT/SRT) and NextRide, a routing app that allows you to chose your route and transportation method. Google Maps will usually provide a bus route as buses get you closest to your destination. I prefer MRT as it's not affected by road traffic, it's faster than the bus, and I don't at all mind walking. Plus I love trains.
Shopping: You will shop at Ikea even if you never really liked Ikea. In Los Angeles I shopped at Ikea when my husband and I moved in together 20 years ago and I think I've been back 3 times. Until now. There is no Target, Restoration Hardware, in Singapore so if you want to buy toilet brushes, towels, and a dresser you will probably go to Ikea because the dresser only needs to last a matter of months or a few years and you probably didn't ship a toilet brush. Ikea has several apps to plan a shopping list, virtually plan your living room, and of course view the catalogue. Also their muesli is pretty good.
Meetup: My first week in Singapore I spent visiting my dog in quarantine. My second week I spent grocery shopping and meeting the gas man and cable man to set up services. So by week three I was ready to grab a coffee with a friend, only I don't have any here. So I applied (many groups are closed and you must be approved after completing a profile) to a few groups and found some meetups they hosted. The first one was a 6km walk with about 25 women along one of the rivers.