Fellow Icelandic learner here, hi!
Firstly - I’m not sure if you were aware, but Icelandic is one of the languages that you can learn for free at a premium subscription level. If you have already paid for a premium subscription but do not need it to learn any other languages, you can ask the developers for a refund by posting a request in the Support & Feedback forum.
Secondly, the main idea behind LingQ is that you learn through exposure to your target language, not so much through exercises. There is a review feature that you can use to reinforce learning, if you want, but the method is mainly based on consuming large amounts of content. As you read and listen to materials in Icelandic, you will soon start picking up vocabulary and sentence patterns. You can also find a short Grammar Guide in the menu (in the lower right corner of the mobile app, or upper right corner in the web app). If you want to practice grammar, I can recommend the LanguageMaster website by @roosterburton.
There are a lot of beginner-friendly materials in the Icelandic Library, thanks to the efforts of Rökkvi Vésteinsson (@rokkvi). If you are learning Icelandic from scratch, I would recommend the following courses:
Íslenska með myndum 0.0 (for learning basic vocabulary) - this course, and the follow-up courses Íslenska með myndum 1.0 and Íslenska með myndum 2.0, have pictures to help you learn. Note that the pictures are only visible in Page View, not in Sentence View.
Íslenska með ljósmyndum 1 & Íslenska með ljósmyndum 2 - more basic Icelandic, this time with photographs.
Einföld Ăslenska - very simple texts in Icelandic. There are also several follow-up courses such as Einföld Ăslenska - DĂ˝r (with short lessons about animals) and Einföld Ăslenska - Matur (with lessons about food).
Íslenska fyrir alla 1, 2, 3, and 4 - a traditional beginner’s course in Icelandic consisting of four textbooks and their audio materials.