* she has decided to learn speaking tactfully and stop being blunt.

* She has decided to learn to speak tactfully and stop being blunt.

* I'm dealing with various hardships in my life that I don't know how to go on.

* I wish I could’ve gone to athe movies tonight with a friend tonight, but none of my friends are keen.them were keen to go.

* She is obviously keenstuck on him.

We wouldn’t use keen in this way:
“She is obviously keen on him being in the group.”

Keen always needs more information to justify the basis of the excited emotion.

‘Stuck’ or ‘crushing’ makes more sense in this context of not much information, however just eluding to an crush of some sort.

Is using "keen" common at all?

In my country (Australia) it is very common.

If yes in what way and in/with what kind of sentences?

* sShe has decided to learn speaking in a tactfull way and to stop being so blunt.

* I was crushed when he said he doesn'idn’t love me any more with that vacant look in his eyes.

* His own economic hardship led him to commit suicide.

We usually take possession of these things “My economic hardship.” When writing about it in this passive way.

* I'm dealing with various hardships in my life and I don't know how to go on.

Do they sound natural?

FYI I speak UK English so my comments are specific to the UK.

* I wish I could go to a moviesee a film with a friend tonight but none of my friends are keen.

Movie = US
Film = UK, although "movie" is becoming more and more common. In any case we would say "see a film" but I'm sure how you wrote it is OK in US English.

* I'm keen on playing the piano.

It's correct but I don't think it's a natural way to say that you like playing the piano.

* She is obviously keen on him.

It's correct but it would be more common to hear "She's obviously into him", "she obviously really likes him".

Is using "keen" common at all?

It is probably more common in the UK than in America, but even in the UK it's not that common anymore I don't think. When it is used, it's more common in the sense of "looking forward to" than "liking" something, as demonstrated in my feedback above.

If yesso, in what way and what kind of sentences?

See above.

* I've always tried to be a tactful person but I'm not sure if I'm considered oneothers think that.

* sShe has decided to learn speaking tactfullyto think before speaking and stop being blunt.

Here it doesn't sound right to use "tactfully". You can say my suggestion or say: "she's trying to filter her thoughts before speaking". Your other sentences sound natural but we use "tactful" to sound well spoken or formal. If you're speaking to a friend, you're more likely to say "She hasn't got a filter" or something similar, it's more common and colloquial.

* I was crushed when he said he doesidn't love me any more with that vacant look in his eyes.

* iIs this seat vacant?

* I'm dealing with various hardshipissues in my life, I don't know how to go on.

I would use "hardship" in your previous sentence because it is a general statement and not about a person, but to talk directly about your own "hardship" doesn't sound natural to me. Issues/problems sounds more natural.

* I wish I could go toand see a movie with a friend tonight but none of my friends are keen on it.

You can only go to places e.g. "go to the cinema", but you can say "go and <verb>" when you went to another place and did <verb>. E.g. if you went to the arcade and played games, you could say "I went and played games at the arcade". Keen generally needs to be used in one of two phrases: "keen on something" or "keen to do something". E.g. "keen on watching a movie" or "keen to watch a movie" but *personally* I wouldn't say "keen" by itself. If you want to read further on this, here is a forum post on this topic: https://english.stackexchange.com/questions/72715/keen-on-vs-keen-to

* She is obviously keen ointerested in him.

I'm sure that it is correct, but we tend to say "interested in someone" to convey the sense of romantic attraction

Is using "keen" common at all?

To be honest, it is quite uncommon in informal conversations from my experience as we tend to use similar words like "interested" (see correction above). Of course, there's no harm in using it.

* The author wrote aboutgave his opinion on this matter very tactfully.

In this particular sentence "wrote about his opinion" makes it seem like he is writing a description or a review of his opinion - I don't know if I'm explaining this well, but "writing about something" implies a sort of distance between the author and what they are writing about, which doesn't make sense when talking about the writer and his opinion because, well, his opinion belongs to him. We would probably say he "gave his opinion" or "presented his opinion" instead.

* she has decided to learn to speaking tactfully and stop being blunt.

In almost every case I can think of, you would say "learn to <verb>", not "learn <verb>ing"

* I'll let you know if the job is still vacant.

I think this is fine, but I would say "the position is still vacant" instead

* I'm dealing with various hardships in my life. I don't know how to go on.

The two parts don't make sense as one whole sentence without a connective e.g. "I'm dealing with various hardships in my life and I don't know how to go on.", or as I did, you can just make them separate sentences.