Is this correct ?
Когда я шла домой, я встретили с ним на улице"
as in 'While I was walking home, I ran into him on the street."

Когда я шла мимо киоска, я купила газету.
as in "When I was walking past the newsstand, I bought the newspaper"

My general question is about the use of unidirectional verbs as a background in the past.
If this is not correct, could you give me some explanations on the matter ?
Also, if you have any precisions to make it sound more 'natural', I'd be more than happy to read them !
Thank you in advance !

Question

Is this correct ?
Когда я шла домой, я встретили с ним на улице"
as in 'While I was walking home, I ran into him on the street."

Когда я шла мимо киоска, я купила газету. 
as in "When I was walking past the newsstand, I bought the newspaper"

My general question is about the use of unidirectional verbs as a background in the past.
If this is not correct, could you give me some explanations on the matter ?
Also, if you have any precisions to make it sound more 'natural', I'd be more than happy to read them ! 
Thank you in advance !

Answer

Когда я шла домой, я встретилАСЬ с ним на улице \=встретила его на улице\ я случайно с ним столкнулась\"
as in 'While I was walking home, I ran into him on the street."

Когда я шла мимо киоска\= проходила мимо киоска\, я купила газету. \= Проходя мимо, я купила газету в киоске\. 
as in "When I was walking past the newsstand, I bought the newspaper".

You use the verb "шла" very well, if that is what you mean, the sentences sound natural. I've just added some more translations. Well done, OnlyWasp.

Answer

1. По дороге домой я случайно встретила его на улице.
2. Я шла мимо киоска и купила газету. ("Когда" sounds weird here, you weren't buying a newspaper on- the- go. First, you were passing by, then you stopped and bought the newspaper.The actions are consecutive.)

Answer

I think it would be better to say the two sentences as follows:
- While I was walking home, I ran into him on the street. – Мы с ним столкнулись, когда я шла домой./Мы случайно с ним встретились, когда я шла домой.
- When I was walking past the newsstand, I bought the newspaper. – Проходя мимо газетного киоска, я купила газету./Я купила газету, проходя мимо газетного киоска.