My mom will hopefully travel to Budapest to see me and check on my living conditions.

We both pine formiss each other.

Pine is correct but not used often nowadays.

Now it’s not quitevery easy to do, thanks to the sanctions.

When there was a peaceful time in Russia, she’d need to go to embassy, apply for a visa, and await for 1-2 months to get it.

Although the process hasn’t changed, it’s got much slower with a lower probability tof succeedss.

Got is British English, Americans used gotten; to succeed isn't wrong but probability of success sounds more natural.

AJust ask my friend: a month backago he got thea visa only for 10 days after 3 tedious months of processing.

Furthermore, the flights gothave gotten quite problematic as there’s no direct flights to EU countries from Russia and you need to overpay quite mucha lot for tickets with a layover either in Istanbul or in Yerevan.

We both pineyearn for each other.

"to pine" most people don't know this word.

When there was aDuring peaceful times in Russia, all she’d need to do was go to the embassy, apply for a visa, and await for 1-2 months to get it.

Ask my friend: a month back, he got the visa only for 10ten days after 3three tedious months of processing.

Numbers under ten are usually spelled out. I don't know why.

Furthermore, flights got quite problematic as there’s no direct flights to EU countries from Russia and you need to overpay quite mucha lot for tickets with a layover either in Istanbul or in Yerevan.