One of them was the skill of socializingmy social skills. One of them was my social skills.

"Social skillls" is the commonly used term.

How the emigration has affected my livfe How emigration has affected my life

I learned how to socialize, as I’d mostly been aloof all of my livfe. I learned how to socialize, as I’d mostly been aloof all of my life.

I’d made all of my friends by just being engaged together in the same school, sports classes, or university. I’d made all of my friends by just being together in the same school, sports classes, or university.

if you want to use "engaged" you can say "being engaged in the same activities together in the same school"

I’d made all of my friends by just being engaged together insharing the same school, sports classes, or university classes. I’d made all of my friends by just sharing the same school, sports classes, or university classes.

I’d made all of my friends by just being engaged together in the same school, sports classes, or university. I’d made all of my friends by just being engaged together in the same school, sports classes or university.

I’d never looked for socializing meetups, as I generally base on the activity which a meetup wmy interactions aroulnd be dedicated toactivities I like. I’d never looked for socializing meetups, as I generally base my interactions around activities I like.

I'm not sure I understand your sentence.

I’d never looked for socializing meetups, as I generally base on the activity which a meetup would be dedicated to (?). I’d never looked for socializing meetups, as I generally base on the activity which a meetup would be dedicated to (?).

I don't quite understand the second part of this sentence.

I’d never looked for socializing meetupopportunities, as I generally basparticipate oin the activity which a meetup would be dedicated toies to socialize. I’d never looked for socializing opportunities, as I generally participate in activities to socialize.

However, after relocation I took up hiking, and I found myself talking to people more. However, after relocation I took up hiking, and I found myself talking to people more.

'relocation' sounds a bit formal; a more common option would be 'moving'

However, after relocationmoving I took up hiking, and I found myself talking to people more. However, after moving I took up hiking, and I found myself talking to people more.

However, after relocation, I took up hiking, and I found myself talking to people more. However, after relocation, I took up hiking, and I found myself talking to people more.

Needless to say, the need forto socializinge is in our human nature. Needless to say, the need to socialize is in our human nature.

And I’dI have quietly begun making new short-term connections. I have quietly begun making new short-term connections.

Again, assuming you are continuing to make these connections, the present perfect is appropriate.

My decision to emigrate affected many piecearts of my life. My decision to emigrate affected many parts of my life.

My decision to emigrate has affected many aspiecets of my life. My decision to emigrate has affected many aspects of my life.

Assuming you are still an immigrant and living abroad, the present perfect is more appropriate.

My decision to emigrate affected many piecearts of my life. My decision to emigrate affected many parts of my life.

After I’d moved into Hungary, I deliberately started attending more social meetups and ultimately found new friends. After I moved to Hungary, I deliberately started attending more social meetups and ultimately found new friends.

Inversely, because moving is a one-time action (you can't continuously move to a country), the past tense is appropriate.

After I’d moved into Hungary, I deliberately started attending more social meetups and ultimately found new friends. After I’d moved to Hungary, I deliberately started attending more social meetups and ultimately found new friends.