Use of “I'd go + verb”

Solution 1:

“I’d go visit my grandmother and make her soup; take her out for a walk and bring her safely back home afterwards […]”

Yes, that is correct. You're using American English, which is fine. In British English, we might say:

“I’d visit my grandmother, make her soup, take her out for a walk, and bring her safely back home afterwards […]”

Note

You need to know the difference between "back in the days" and "back in the day"

The singular is used when the phrase is used alone to indicate an unspecified period, e.g.

"Back in the day, I used to …"

versus

"Back in the days of Kings and Queens, life was much more …"

"Back in the days before the internet, life was much more …"