All of the options from 1 are okay, however for 1c, "She tries to follow the latest trends when buying clothes" sounds better.
2a is good - It's actually perfect.
2b is good, however its meaning is slightly different from 2a.
2c is bad - the "still" doesn't work, and if you remove it, you get "my father has worn the jacket that was in fashion ten years ago". This sentence is past continuous, not present continuous, so its meaning is different. It implies that your father, in the past, wore a fashionable jacket, but it makes no claim on what's going on in the present.
2d is good.
All the sentences in 2 have slightly different meanings. I'm sure you know this, though.