Task No.1
Yes there are many games which are used to practise grammar, to make practise activities more interesting and motivating for students.
I like "Find somebody who". Have you ever visited + different countries?
after Christmas - Have you eaten carp? + other questions about Christmas
Did you .... at the weekend?
Do you + everyday routine, interests, sport...
Sometimes I do not organize it Find somebody who, but just answer the questions with your partner, report about your partner.
I like using diggerent quizes, crosswords etc.
It is necesssary ti make the lesson more enjoyable, more interesting
Task No.2
i very often use pair work (more than group work, my experience, students do not want to speak in a group, some of them can relax), or work in three people. After a set time I ask some of the students, I do not ask about them, but about their partners, so everybody has to talk in the pair. If there is an exercise in our coursebook good for personalising we do it, the best way is to talk about our own experience. For teachers it is necessary to know something about students, their families, friends adn hobbies, plans etc. When we star a similar exercise I can start answering questions, students should know something about me as well.
E.g. At the weekend I did.... What did you do at the weekend? Practising past simple (was/were, regular, irregular forms, ..).
Very often I use gap-filling exercise, correcting mistakes exercise (more difficult), which are written productive-practise exercises. Feedback is usually organized in pairs first, then class checking.