1 . a) sitting, talking, writing, drinking, lying, meeting, cutting, feeding, flying, cleaning, eating, teaching, watering, typing, playing.
b) dying, shaving, hitting, reading, crying, travelling, listening, baking, snowing, raining, staying, dancing, living, fishing, having.
2. a) opened, loved, planned, emptied, stopped, studied, played, kissed, robbed, changed.
b) arrived, tidied, laughed, travelled, hurried, posted, started, looked, pushed, watched.
3. a) 1. Sam will visit/is visiting his friends this weekend. (То же самое что и в пятом предложении в следующем пункте - b, лучше использовать второй вариант)
2. She takes her daughter to school every day.
3. Be quiet. The father is sleeping.
4. Water doesn't boil at 50 degrees. (Не уверен, что сделал правильно)
5. He is watching TV now.
6. The bus is leaving at 6:30 pm.
b) 1. She doesn't like flying by plane.
2. Tom is looking very stressed.
3. He is studying a lot these days.
4. My train is leaving in an hour.
5. I will meet/I'm meeting my friends tonight. (Частично неправильные времена, в контексте данного задания лучше использовать второй вариант)
6. She will work/ will be working in a library next month. (В задании указаны неправильные времена)
4. a) 1. I've tidied my room.
2. She has been writing a book for a year.
3. They have been living in Rome since 2016.
4. I've met V. Putin.
5. They have been travelling around Italy for ten days.
b) 1. They have been staying in the Park Hotel for a week.
2. My sister has just travelled round the world. (Неправильно и непонятно составлено предложение, но в любом случае я указал правильное решение)
3. He has never been to Moscow.
4. The children have been sleeping since 5 pm.
5. We have seen A. Pugacheva.
(P.S. на всякий случай подчеркнул слова, которые помогли определить время - только к 4-ому заданию)