Most public transportation companies in Sweden have websites and apps in English where you can purchase both single and monthly tickets as well as learn about any discounts.
Skånetrafiken (includes Lund and Malmö)
Most of the healthcare information you find online will be in Swedish, although some information is available in other languages. 1177.se, for example, has some of its content translated into 17 languages, and the web page will link you to other helpful resources.
For dental care, you can search for 'folktandvården' in your city to find your local public dental care venue. If you have a Swedish personal number, you can also create a personal account on several sites and book appointments online. Basic information about dental care in Sweden in the link below.
This popular web-platform is designed to enable you to meet people with similar interests as yourself. Here you can, for example, find the next events in your area of interest: from IT-startups and web programming to knitting and scrap-booking.
The biggest Swedish online-shop purveying tickets for a wide range of events is Ticnet.se. Here you can find good deals to a great variety of concerts, sports, festivals, fairs and exhibitions.
5. Local services
Blocket.se (in Swedish)
Basically, this website is the 'Swedish craigslist' providing classified ads in different categories ranging from housing to clothing. Also a great platform for cheap second hand electronics or furniture.
Swim and exercise (in Swedish)
Public gyms and swimming pools are very widespread in Stockholm and most other Swedish cities. The site above is for Stockholm, but you can normally find information about the public sports facilities in you area at the official webpage of the city administration.